DE7417268U - EDUCATIONAL AND ENTERTAINMENT GAME - Google Patents

Description

1. Prof. Dr. rer. nat. Manfred Eigen
3400 Göttingen, Georg-Dehio-Weg \ A

2. Dr. techn. Ruthild Winkler, née Oswaritsch 3431 Berle ^ ch über. Witzerthauseri

"Educational and entertainment game"

The invention relates to an educational and entertainment game, which differs from the usual parlor games through a variable combination of chance and law and thereby offers the possibility of representing the reality of natural law. In the conventional games, like checkers, chess, mill, halma, go, nim, etc., are specifically a / 'f elements (board, figures, dice) tailored to the respective game are used.

In contrast, the invention is based on the object of a set of game elements to create with which a variety of entertain- ment and / or educational games can be carried out in connection with rules, in the

7417268 13.0177

The nature of the observable processes. This allows physical, chemical, biological, sociological and other processes to be simulated and made understandable in a playful way. So becomes one about the mere The educational purpose of the game is ensured, an effect that can be achieved more with conventional parlor games. Lsi, uu iiire rcycin have arisen historically and they do not represent simple facts that can be directly interpreted scientifically.

According to the invention, a set of game elements is used for this purpose Application, which essentially consists of a base plate, several templates to be applied optionally to this, representing the respective playing field with co-ordinate numbering, several differently marked game stone groups and random number generators corresponding to the respective co-ordinate numbering of a template, in connection with Rules that determine the stakes of the various game ducks in the individual games.

A support plate for the game pieces to be attached to the base plate or the playing field templates is preferably used, those with depressions, holes or the like. provided or from a grid is formed, corresponding to a field division common to the Spielfeidschablonen. This support plate is particularly advantageously made of transparent or translucent material. On the other hand, it is possible to manufacture the base plate and the game pieces from magnetizable material or to design them as permanent magnets. For fitting the individual play elements on top of one another, the base plate or the playing field templates and the support plate stops, recesses, brackets, bezels or the like. Provided.

A further improvement is given when the base plate or a playing field template, preferably forming square fields

7W2M ικπ

The grid supports and the set of game elements through differently sized cover frames is added, each of which has a different numbering of coordinates.

It is particularly useful; when the base plate flooded the floor

Box forms, the side borders of which are mating surfaces for the playing field '

templates and represent the support plate for the game pieces. I.

The fields divided by the grid can be customized with an individual Be provided with lettering or numbering. As game pieces get preferably Glass spheres and, as random number generators, various pairs of cubes in tetrahedron, cube, octahedron, dodecahedron, icosahedron or like - shape with area numbering or symbol lettering for use. But you can also use the numbering of coordinates by means of gyroscopes, roulette discs or the like corresponding designations or codes corresponding to the rules of the game.

The fields of the base plate, the game pieces, the random number generators or the playing field templates can be labeled with various code systems which are related to different physical, chemical or mathematical systems.

In addition, in some games there are auxiliary elements, such as on the game pieces or attachments, cones, frames or other markings to be attached to the support plate for the specific identification of the game pieces, playing field regions, such as B. defined neighborhoods or the like. Provided. In addition, you can also play pieces with coupling elements to their mutual Use connection.

The complete game set is divided into several sections according to a superordinate principle divided. The individual play units provide both entertaining board games as well as challenging educational games that are aesthetically pleasing

7417268 13.81.77

Design and intellectual content appeal to all ages. A Understanding of the teaching content starts in the elementary school years. A deepening takes place later, as soon as simple mathematical relationships are understood and their relationship to basic phenomena recognized in physics, chemistry and biology = From this level ου? leads the game collection up to the current problems of research. It expresses in particular the probability character of physical laws. The relationships, which have hardly been explored in terms of their consequences Other areas such as biology, computer science, social sciences or even art are addressed. Significant is, however, that "playing" itself does not require any special knowledge. The decisive difference to well-known board games, like mill, checkers, halma, monopoly !, chess, go, etc., consists primarily in the fact that the underlying rules are simple mathematical and physical Gf -.- correspondence that initially unconsciously - playfully - come into play. Comes in his diction the game according to the invention Hermann Hesse's idea of the "glass bead game" is close:

"These rules, the sign language and grammar of the game, represent some sort of sophisticated one Secret language ... which contains the contents and results is able to express almost all sciences and to relate them to one another. "

It corresponds to this diction when as characteristic elements of the invention Glass beads can also be used in the game. The glass beads only begin to "live" through the idea through which they are placed in the respective Interact with each other. This idea is embodied by a combination of law and chance realized in nature.

7417268 13.8177

1. The game idea υηα its scientific basis

The principle of the game collection is based on the fact that material elementary processes cannot be precisely predicted due to the uncertainty principle of quantum mechanics (Heisenberg principle). Every single event can only be described by a probability statement. This (limited) indeterminacy (of the elementary processes) is simulated in the game through the use of dice, the dictation of which is subject to the individual units of matter represented by glass spheres. Since many such elementary processes interact in every game and only thereby determine the outcome of the game, this can be regarded as representative of a macroscopic event that is accessible to observation. It can be any physical process, chemical transformation, biological mechanism, or sociological phenomenon. This macroscopic process, based on a large number of material elementary events, may well show deterministic behavior. As soon as a probability distribution is known, reliable expected values can be calculated for populations with large numbers. This principle is ultimately also the basis for the calculation of every insurance company. On the other hand, there are events - in physics they are called! Nstabilities , in normal parlance "catastrophes" - which even in their macroscopic appearance cannot be predicted. Whether such "catastrophes" can occur in nature depends solely on the retroactive effect of an indefinite statistical fluctuation, which initially appears in the elementary area, on their own development.

The effects of statistical fluctuations can be broken down into three basic types characterize. With the help of the games, these can be shown particularly clearly will:

a) A fluctuation deviating from the mean value behavior has the tendency to reduce. For large populations, the result is a stable macroscopic behavior characterized by deterministic expected values.

7 * 1726 «13.81.77

b) The fluctuation has no influence on future development of the system (game). The macroscopic behavior is random, all possible states become more unpredictable Result in appearance. One can say that the system performs a "random walk".

c) The fluctuations tend to increase. Here the microscopic fluctuation becomes the cause of an im macroscopic scale v3uiffeienden "catastrophe" »

Since it is indeterminate whether such a self-reinforcing elementary process takes place during the observation time, in case c) the microscopic indeterminacy of an individual elementary process occurs macroscopically immediately in appearance.

If a Mareriesysrem wants to remain stable in a state, it always has to the behavior of the self-regulation of fluctuations described under a) be fulfilled. Everything that is called "equilibrium" in physics and chemistry is of this kind. The behavior of such a macroscopic one The system is essentially deterministic, i.e. also within a specifiable one Predictable limits. The difference is the selection-based evolution of living structures or even the evolution of these Ideas strongly influenced by unstable diets, even requiring progress such "catastrophes" in the elementary sector.

In the first game section, the different cases of fluctuating behavior are contrasted with one another and it is shown how evolution from a series of instabilities arises, each of which breaks the system into a transferred to a new metastable state of higher information content. That later Entertaining parlor game yet to be described: "Survival" closes this section. This game resembles "Go" in some ways, whose

7417268 13.0177

Rules, however, are arbitrarily subordinate to the strategic aspect alone and do not describe a simple natural process.

In the second section there are specific interactions between individual glass spheres were introduced to reflect the statistical elementary events give a certain preferential direction. The natural processes represented by abstract rules can consist of static force effects as well as dynamic conversions result. The resulting patterns then describe both "conservative" - i.e. H. on static force effects based - as well as so-called "disslpative" structures. These are patterns that can only be sustained through constant transformation be able. In chemistry and biology there are many examples of such, structures resulting from dynamic interactions. Mention should be made of biological "clocks" that are produced by cell differentiation and morpho-nesis expressed "shape" of the organisms or even the complex ones Patterns of excitation in the central nervous system, which become apparent through the structuring of "fields of perception" in the cerebral cortex ·. One for this section Typical parlor game: "Struggle", which deals with a classic reaction example from chemistry and ecology, is more detailed in the appendix shown.

The third section deals with evolutionary processes, starting with molecular biology through population genetics to the evolution of ideas. The selection processes dealt with in the first section form the basis. The general question is: According to which criteria does a selection take place in nature; How is that what we later call "information" - if we recognize it as meaningful - come about? One of the games in this section shows that, first of all, stabilizing forces promote the selection of certain structures. So you can z. B. the molecular interactions between the four fundamental

\ stones of the nucleic acid molecules carrying the genetic makeup by suitable

; Simulate the rules of the game. The amazing thing is that among those involved in the game

7417268 13.9177

- 3

Molecular structures that are victorious that have been selected in nature, e.g. B. cloverleaf structures of the " ^r ansfer nucleic acids or flower-shaped structures of certain phage variants. Of course, this is by no means" astonishing "for the molecular biologist, because only the rules unrelated to nature were used in the game. More complex structures occur in protein molecules twenty basic building blocks, a similar complexity is to be expected as with the language structures, which are composed of a comparable number of basic building blocks, the letters of the alphabet

full of words from arbitrary letter distributions is demonstrated. The coding laid down in the genetic makeup and its formation can also be simulated in the game. Here four different types (colors) of glass beads and three tetrahedral cubes, the four faces of which are colored accordingly, would be used. In abstract terms, the alphabet of our genetic information consists of such combinations of three. These in turn represent a letter of the alphabet in which the functional properties of living systems are written down.

Glass bead games can represent coding and information transmissions in a variety of ways. If tone intervals are coded with the help of the glass balls instead of letters and if certain composition rules are applied during the selection - for example as they were once put together by J. Ph. Rameau for the Mi.'sik of the classical period - this results in sonorous tone sequences. Even more complicated network structures, which have the property of information storage and dbs adaptive learning, can be simulated on the game board.

The fourth and final section is the sociological aspect of evolution dedicated. Exponential growth laws were used in the preceding Sections discussed repeatedly. Population explosion, pollution,

7417268 13.0177

but also increasing prosperity follow such principles. In the Publications en: "Club of Rome" was uncontrolled on the dangers Insistently indicated growth. The glass bead game according to the invention Having a realistic background can make these perspectives with more terrifying Demonstrate clarity. However, a more detailed analysis of the growth laws also shows the limits of simple extrapolations. The "Stationary equilibrium" recommended by the "Club of Rome" includes d «e Possibility of instability, as explained in the first and second sections. In order to prevent disasters, therefore, an extensive clever scheme. Conjure up blind production cuts, just like « unbridled growth, the danger of its collapse.

The overview given here shows that such a versatile game collection constantly combining to create new variants! The imagination are No wicnZcn set.

For this very reason it is also possible to use most of the conventional To accommodate board games in the collection. Stencils for "Go" ^ "Chess" ("Dane"), "Mill", "Halma" and other games are therefore also provided. This is especially true for some in public lesser known "math" games. For example, the "Life Games" developed by the English mathematician Conway are particularly good play well on a ball board with different colored glass beads. Variants of this game that Conway's missing element of chance are described in the "game book". Also the well-known "Nim game" - a prime example of the J. v. Neumann and N. Wiener developed game and machine theory - can be transferred to the ball board with many variants that are particularly interesting for the theory.

2. General description of the game

The parts forming the play element set according to the invention are shown in FIG accompanying drawings in exemplary embodiments - on which the invention is not

- Un

should be limited - reproduced and in their use based on some Game instructions and rules explained below. B show:

FIg. 1 a perspective view of the basic floor plan with

additional playing field templates and perforated plate;

2 to 9 plan views of different embodiments of playing field templates;

10 shows a section through the base and support plate with attached

Bullets;

Fig. U different groups of game pieces (glass balls);

FIG. 12 shows different forms of randomness generators; FIG.

13 different marking elements and

14 to 19 are schematic representations of various game situations.

The game elements common to all sections are:

Several sets of differently marked pieces, such as. B. Groups (about 20 to 30 pieces) of different colored glass balls la, Ib ... according to Fig. 11;

A support plate 2 with, for example, (12 χ 12) - (20 χ 20) rows of holes for the optional insertion of balls 1 a, 1 b, 1 c etc.

Various templates 4-13, which can be used individually or e.g. T. also together Define a playing field arrangement adapted to the rules (Fig. 1 to 9) and for this purpose z. T. are provided with individual coordinate numbering. These templates represent - in conjunction with the

, 7 * 17281

respective game instructions - the element of the law to which the individual course of the game is subject. In order to ensure that templates 4-13 and perforated plate 2 are properly aligned, an additional iirunapiane 14 ίπίί corner or RcmdsiruGiiur.ger; 15 ξ ^: -γ application, which can ultimately also be used for filing and storing all templates and other play elements. The templates required for the respective game are placed on top of one another on the base plate 14 and finally covered with the perforated plate 2.

When the base plate is designed as a permanent magnet or from consists of magnetizable material and game pieces, for example in the form of platelets made of a material corresponding to the base plate material are formed, the perforated plate 2 can also be omitted. On the other hand, playing field templates can be made from a grid with numbering of coordinates (Fig. 2) exist, replace by a template 4, with a continuous grid over the entire surface ur - = s <- 'nen frame 5, which has a play area from Z. B. covers only 8 χ 8 fields (Fig. 1) or 10 χ 10 fields, and carries the associated coordinate numbering.

Random number generators are also required for the playing field templates. These can be, for example, sets of cubes or pairs of cubes in the form of the five Platonic solids: tetrahedron 16, cube 17, octahedron 18, dodecahedron and icosahedron. One cube of the required pair of cubes is appropriately numbered in red, for example, and the other is black, even if the numbering of a coordinate on the associated template is red and the other is black. In each F _a ll (10 χ 10 fields corresp. Fig. 9) for a decimal system can icosahedron with two like-numbered surfaces require to use. So here one dice (red numbers from 0 to 9) would represent the tens 0, 10, 20 ... , 90 and the other (black numbers 0 to 9) would represent the ones. The same is good for any other number base, i.e. 4 for the tetrahedron, 6 for the cube, 8 for the octahedron, 12 for the dodecahedron

and 20 for the icosahedron ,. These cubes represent the element in the game of chance. Instead of the pairs of dice, you can also use roulette discs, Number gyroscope or the like can be used.

The individual game sections are built according to a logical scheme which is described in a game book. This not only contains the instructions for each game, but also explains why the rules are so and were not chosen otherwise, so that they describe a certain physical, chemical, biological or sociological phenomenon will. Because the complete game set is put together according to a modular system the collection can be expanded at will.

In order to additionally mark certain game pieces or balls or to mark certain Kygeigruppen or game fields ¹ ″, marking parts are also used, as shown in FIG or 21 They are used in various embodiments when it is a question of highlighting or delimiting certain groups of spheres The use of these parts will be discussed in detail later.

3. The game sections - arranged according to their scientific basis. Overview;

I. The statistical laws of physics and chemistry

1. "Balance": The game demonstrates the setting of a

stable equilibrium in which statistical fluctuations always have the tendency to reduce »It is based on a model set up by the physicist couple P. and T. Ehrenfest. The same-

741721 «

2. "lrrfluc":

3. "Disaster":

- · 13-

weight is illustrated by a spherical distribution that can be predicted within narrow limits on the game board.

A slight change in the rules of the game increases the self-regulating character of the Fluctuations. If you introduce a "head or eagle" decision, it drifts Ball population through all possible occupations of the playing field.

Another change in the rules of the game now causes fluctuations to become one "Swing up" the avalanche. The system jumps irreversibly across all limits, one occurs Disaster one.

4. "Selection":

A combination of the rules of the three previous examples has the effect that im System, certain glass spheres selected and held in a (meta-) stable state will. Some fluctuations, however, can lead to the breakdown of such a metastable State by selecting a new type of ball.

This behavior occurs even if the individual varieties are in their physical Properties (probabilities) do not differ from one another. Even then, one becomes initially multicolored distribution a single color read out and (meta-) stably reproduced ("survival of the survivor").

7417281

Do the different types of balls differ in their individual properties, "fittest" in the sense of Darwin dt.wh is a defined mean value behavior.

5. "Survival":

- Leave the educational games described above. a fascinating board game combine that can be played by several partners in competition. It reflects all of the items mentioned under points 1 to 4 physical laws. The outcome of the game is unpredictable and depends on the strategic skill of the player.

II. Structure, pattern, shape. 1. "Cooperativity": There were no pronounced distributions in the statistical distributions mentioned in Part I. spatial structures or patterns. By introducing interactions between With the glass beads, the different colors now appear in coherent regions. It can even lead to complete "color changes" (Phase formations) occur when the interaction forces are sufficiently strong. The laws of this "cooperative" Conversions are simulated in-game.

2. ", reaction structures"

7 * 17281 Here a large number of chemical reaction mechanisms can be traced on the board, whereby the glass balls

represent different chemical compounds. A particularly interesting board game becomes from the well-known Lotka-Volterra reaction derived. It obviously has parallels in ecology and genetics. The What is impressive about this reaction is that the populations of the reactants oscillate or form spatial patterns when a directed movement is superimposed.

3. "Cell differentiation and morphogenesis": The type of reaction described in the 2nd game - applied to self-reproducing cells - is ultimately responsible for the process of cell differentiation _/ org-m formation and morphogenesis. The process corresponds to the pattern formation of a periodic reaction in flow gradients. The results of experiments on the formation of shapes in amoeba and hydrazoa can be visualized on the ball board.

4. "Excitation pattern": The storage of optical stimuli in the form of excitation patterns takes place in the cerebral cortex according to similar laws. This is currently the focus of interest in neurobiological research standing process can be recorded with the help of a game.

5. "Symmetry": To represent the spread itself: self-reproducing Suitable placement games are demonstrated for patterns. Also more recent work in the field of cellular automata can be explained like this.

7 * 1726 «υ egg.

• tr- '"

-Id-

III. Evolution, or the

Creation of information

1. Evolution of genes The reproduction of nucleic acids is made with realistic empirical values simulated. It turns out that certain structures are advantageous and proceed as a winner out of the competition. This process becomes a interesting board game designed. The structures created in this game are correct mii those found in nature and (first in recent years). The game has three variants: a) Simple Base pair structures, b) symmetry as a result of complementarity, c) recombinant Exactly (sexual reproduction).

2. Evolution of complex structures and coding

Protein molecules - from which the immense diversity of living nature has emerged, are in their complex, unmistakable diversity quite comparable to the structures of our language (word and sentence combinations). There are about 30 letters of the alphabet opposite the 20 protein building blocks. In both cases, the enormous number of variations results from a hierarchical structure. The initial situation for the evolution of these structures is characterized in a clear game of "competition for words". Another evolution game demonstrates - again using the example of language - how meaning arises from "nonsense". The parallel to the evolution of functional protein structures is shown.

7H7268 13 017?

The rules according to which you choose are important. Rules of composition, for example, applied to a statistical tone sequence, transforms this into a sonorous sequence.

3. Information transfer and storage. Adaptive learning. Securing information t, eger. Fluctuation losses can be achieved with the help of certain realities will. These can be worked out into interesting games in which secret Exchange and forward information will. Also models for the storage of information in self-organizing networks (see 11.4) are specified

IV. Society and environment

1. Laws of growth The various (linear and non-linear) Laws of growth are demonstrated on models. In one of the Conway life games outgoing competitive game becomes the interference between growing population structures shown.

2. Optimization Some games based on von Nsumann's Game and optimization theory are presented.

3. "ROME" The "Club of Rome" game across borders of growth.

The game is essentially based on the growth laws discussed below. Realistic Influences are in a parlor game

741726 «around.

shown. Criticism of simple extrapolations is substantiated by game situations in which shown becomes that, due to instabilities, predictions can be made impossible.

4. Examples of game instructions with explanations 1. Example: Survival game: "Survival"

Game instructions: "Survival" is a competitive game for 2 people. The players take turns placing glass balls of their color in a playing field marked with numbered coordinates and then roll the dice to determine the fate of these balls. Birth, death, competition and the safeguarding of living space characterize the course of the game, which admittedly takes place according to certain rules, but on the other hand leaves the player enough freedom to skillfully exploit the random decision of the dice in his favor. The winner is whoever has most of the glass balls ^{in a "safe" position at the end of the game.}

Preparations: The playing field template with 8x8 fields and the corresponding Coordinate numbering (horizontally in black and vertically in red) is applied. This includes a pair of octahedron cubes with a corresponding (red and black) numbering. Each pair of numbers rolled corresponds to one Field identified by the relevant coordinate assignment on the template is marked. All fields can be rolled with the same probability.

Each player receives balls of a certain color.

Course of the game: At the start of the game, the ball board is empty. The players now alternately place one ball each. If a player completes a "survival"

7417268 01/13/77

Region (s. Υ.), He may have any, but not in a "survival position" remove the opponent's ball. This ball goes into the reservoir. Likewise, "encircled" enemy balls (see below) turn the reservoir fed. Overall, however, each player is only allowed to use his original Place pre-red on balls (32 pieces for! 2 players) - regardless of how many of its spheres have already migrated into the reservoir during the occupation phase.

When the players have placed all their balls, the dice begin to roll - strictly alternately. The following rules apply here:

1. If a player rolls an empty field, he may place a ball (of his color) from the reservoir on this field. If there are no more balls of his color in the reservoir, he may open one of his unfavorably placed balls transfer the field rolled. All of its glass balls should be secured in place Regions are located, the player must pass.

2. If a field is rolled that is occupied by an opposing ball, so this must be removed, d. H. it comes into the reservoir. The ball can only turn away when not in a survivor position lies.

3. If a field is rolled by its own ball - indifferent in which configuration - is occupied, this may turn twice. To do this, (from the reservoir or from an unfavorable position) your own ball in any empty space. In this case the successful Players roll the dice again, again following the rules. If one is still lucky, this procedure can go repeat as often as you like.

741726 «η.w.77

-20- .7 /

The meaning of the fields: At the beginning of the game all fields are equivalent. However, this equivalence is canceled by the occupation.

a) Survival positions If there are four balls in a region that consists of

at least four ZwSGrr.irianhcngerid, squarely arranged fields i

stands (Fig. 14), then these are "stable" and can no longer die out, I.

unless they are made unstable by enemy encircling maneuvers j

(see below). These block-like "survival regions" can expand, f

z. B. two additionally occupied fields result in a new block (Fig. 15). i

At the completion of each new block of four, the opponent is allowed one j

any non-rod ball can be removed, which is then put into the reservoir j wanders. The only decisive factor is how many blocks through the relevant

Zuy are each completed (regardless of what is already there), (Fig. 16). ι

b) Enclosure: When an opposing region is completely encircled, may it be cleared, d. H. these balls migrate into the reservoir. When

■ Surroundings are only valid for closed, occupied rows of spheres with orthogonal ones Edges, i.e. Fig. 17 a, or Fig. 17 b, but not Fig. 17 c or Fig. 17 d, If the encircled region is a survival position, it can become unstable, if the encirclement ajs as many orthogonally connected blocks as fields are in the encircled block region; z. B. Fig. 18 α or Fig. 18 b. Also Fringing fields can be surrounded; they must be framed by at least three corner fields from 2 sides, as in Fig. 19α or Fig. 19b. for Survival regions on the edge of the Spieifeidrand apply the above-mentioned encirclement rules in an analogous way.

Game conclusion and evaluation: The game ends as soon as - after placing all 32 balls - a player has placed all of the balls belonging to him in stable positions ("survival" positions) in the playing field. Each player can then fill in the empty spaces surrounded by them with balls. All balls in survival regions count as points; the winner is the one with the highest number of points. In a tournament, each player's scores are added up.

741726 «

Interpretation:

The game resembles - purely outwardly - a number of well-known board games, especially the Japanese "Go". This is especially true for the initial phase of the game, in which the balls are placed according to certain strategic aspects be set. This phase only serves to build up a starting position that is more or less advantageous for the individual player. The actual selection game begins with the roll of the dice, whereby all possibilities of statistical fluctuations can occur due to the rules.

First there is the rule that an empty one (hit when rolling the dice) Field occupied, but a field occupied by the opponent may be cleared. This rule, taken by itself, would be a stable mean one Cause occupation as they z. B. is illustrated in the equilibrium games. If many fields are occupied, many are cleared, if, on the other hand, only a few fields are occupied, the chances of a new one are high. This new generation - simulated by filling empty fields but would be similar to "spontaneous generation". This occurs with a higher population density hardly any weight. The law of multiplication of living structures, on the other hand, is of an autocatalytic nature. Creating new structures is one Reproduction of already existing ones. This means; only where living beings are already present, more can arise, and more so, the more already there sindi (at the same time, of course, more people die accordingly). The rule according to which a field occupied by its own sphere can be doubled takes this "autocatalytic" law of multiplication into account, to which all living beings are subject. Would birth and death be exactly proportional to the number of occupied fields occur, the population density would fluctuate uncontrollably, as is clear in the "Irrflug" game (1.2.) come to expression! - »

For this reason, additional hesitation-dependent "selective" Advantages "introduced: survival regions, repeated dice, encircling

7417? 6 «n.m. 77!

etc. These enable aisweichende from the law of linearity tendency that affects in the form of a favoring of the player (birth and death rate are no longer strictly linearly dependent on & Besetzungsdichre). This brings the possibility of instability, or rather a catastrophe, into play, which ends with the extinction of a type of ball.

That becomes clear when one looks more closely at the laws according to which Reproduction and death occur. An increase in the number of balls of a certain variety increases the likelihood of further doubling. at This means that the player has enough survival regions can train, but his opponent is constantly losing balls. The death rate of one's own balls no longer increases proportionally to theirs Occupation, since most of them are protected in survival regions, and this one expand cooperatively too. All this together leads to the disaster law shown in the third game (1,3). All three Influences, stabilization, drift or instability work in this game as in natural selection with. It depends solely on the configuration - resulting from random decisions - which influence there is eventually prevailed. The survival game therefore often includes a distribution similar to "Pat". But there can also be "disasters" occur in which possibly all balls of a game partner die out. The occurrence of such disasters can be limited to some extent control through the game strategy, and that makes "survival" an interesting one Board game.

2nd example: "Struggle"

How to play: "Struggle" is a transformation game that consists of phenomena represents the field of biochemistry and ecology. In this game! it is important to convert one type of ball (green) into another type (blue) via intermediate carriers (yellow and red). The blue balls count as

Profit points. The game can be both cooperative and competitive play between 2 or 4 people. The through characteristic conversion mechanisms The marked course of the game can become very rapid towards the end and diverge in extreme oscillations in the cast density Express ball types. Two versions are described below In the first version, two people play cooperatively on a field. (It can therefore also be carried out by one Süieler alone.) The Players only compete to win blue balls, they but do not hinder each other. Yes, advantages of a specific game configuration can be used by both players - according to the size of the die. In the second version, each player can have his own Build up the field and thus bring strategic moments into play.

Preparation for the game: 1st version: You use the template with 8x8 or 12x12 fields and numbering of coordinates, plus a corresponding one Litter pair (octahedron or dodecahedron). It stands one through the number the playing fields limited reservoir of green, yellow, red and blue Balls available, from which the players collectively (e.g. alternately) at the start of the game 16 (or 36) yellow and 4 (or 6) red balls and in the Place the playing field.

2nd version: With 4 players you use the template shown in Fig. 3 and corresponding pairs of cubes (octahedra or cubes). Here, at the beginning of the game, each player places 16 (or 9) yellow and 4 (or 2) red balls in his playing field section. The overlapping regions may be used by all adjacent players. The way in which yellow and red balls are distributed (especially in the border area of the overlap region) is of - possibly crucial - importance for the game.

Course of the game: For the further course of the game, the term 'neighborhood' important. All 8 fields bordering a central field, i.e. both the four orthogonally and the four diagonally adjacent fields, are considered "neighboring fields" Fields.

74177B "

1. Version: The players take turns rolling the dice and acting according to the following Rules:

1. If an empty field is rolled, regardless of the "neighborhood" - a green ball can be placed in the relevant field.

2. If a field is hit that is already occupied by a ball, the player may a conversion can be initiated. The following then applies:

a) If the ball hit is a yellow one, and is there in the neighborhood empty fields, another yellow ball may be placed in one of the empty neighboring fields and then after Rege! 3 will continue to proceed. (The The meaning of this operation is as follows: The yellow ball on the field hit has the one that actually comes into play first green converted into another yellow, which is now on any of the neighboring fields placed and possibly react immediately from there // pus can.)

b) If the ball hit is a yellow one and is on a neighboring field a green ball, the green ball may be converted into a yellow one. Then rule 3 is applied again. Here rule 2a takes precedence before rule 2b.

c) If the ball hit is a green one, the green one may - provided that a yellow ball sits on one of the neighboring fields - are also converted into one! τ. Then again rule 3 - if the conditions are met - to be further converted.

d) If the ball hit is yellow, it is in the neighborhood a red ball, the yellow ball may be transformed into a red ball and also continue to react according to rule 3. Here rule 2d takes precedence before 2a and 2b.

741726 * nm.77

C ^r ' - 25 - JJ

e) If the ball hit is a red one, it can either go into a blue one and these are removed from the game in favor of the player concerned. Or - if a neighboring field is occupied by a yellow ball

j is - dart this iNachburkuyci into a roic woundcii wcrdcr ·· DSs decision, which of the two options has priority is up to the player. Only in the second case may the player proceed according to rules 3 and 4. In the first case, the blue ball is credited to his account.

3. All balls resulting from a conversion under Rule 2 a, 2 b, 2 c, 2 d and 2 e emerge, can react directly if the following conditions are met are met: In the immediate vicinity of the due to Conversion of a new ball coming into play must be a ball, with which it can react. That is

a) for green: a yellow one

b) for yellow: a green or red

c) for red: a yellow one

Therefore, the green ball becomes a yellow ball and the yellow ball turns into a red ball transformed, no matter which of the two bullets was hit or the neighboring ball was hit. In other words, green-yellow from neighboring balls becomes yellow-yellow, from yellow-red to red-red. This process can repeat as often as you like. Green and red (as well as green-green, yellow-yellow or red-red) do not react with each other. The neighborhood always relates on the sphere resulting from the transformation. If the prerequisites are particularly favorable, the reaction can develop before the pus is thrown propagate all over the playing field. This is very often the case towards the end of a game. There are then strong oscillations in the line-up the different ball colors (especially yellow and red) and with it drastic changes in the chances of winning. V

7417268 1301.77

4. For each conversion from yellow-red to red-red (rule 2 e; 2nd possibility) the player concerned may roll the dice again specifically for a conversion from red to blue. (This throw is only valid for such a conversion), If a red ball is hit during this throw (other hits do not apply) _y this can be converted into a blue ball and credited to the player concerned. In the case of a yellow to red chain reaction, it is advisable to place all the yellow balls exchanged on the edge of the game board. For each of these balls you can then make another throw.

2nd version: The rules are completely analogous to those of the first version. However, each player only rolls the dice for his region. The various conversion reactions can, however, propagate beyond the borders. One must therefore strive to use one's share of the overlapping region as well as possible, without however "igniting" a transformation that can propagate far into the opposing field, where it only works for the benefit of the opponent. This, in turn, will try to conjure up this possibility at any time due to the occupation of the field.

End of the game and evaluation: The game ends as soon as one player has all red or yellow balls. If there is no more red ball on the playing field, no more can be created. The same goes for the yellow balls. As soon as these are used up, no more green balls can be converted, nor new red ones Spheres are created. Only the existing red balls could still be converted to blue. The blue balls acquired by the players count as winning points. What counts in a multi-player game every blue ball two, every red ball still in the relevant section at the end of the game one point. The winner is whoever has the highest number of points achieved.

-27 interpretation:

The rules of play look relatively complicated at first glance. they are but very much! can be learned, especially when it comes to playing! shows the problem presented. It is a well-known reaction scheme for an autocatalytic chemical conversion that according to its discoverers Lotka-Volterra reaction is called. This reaction can be in the form of Oscillations run off. It is believed that they have many biochemical control processes, so-called "biological clocks" is the basis. The same reaction concept also describes a specific ecological one Sirutation. Based on this, the scheme should be made plausible. Let us imagine the following environmental situation:

1. Grass grows green balls come onto the playing field.

2. The grass is made of bunnies green ku -! N can - only in eaten, and the rabbits present yellow balls in multiply. yellow balls are transformed.

3. Foxes can eat the rabbits yellow balls - in turn and reproduce only in the presence of red balls

be turned into red balls.

4. Foxes are hunted. You can use red balls if you can die out, be hit, out of the game - The fox fur is the field to be taken «The blue Trophy or winning balls ("blue fox") are that

of the hunter. Profit.

It should be noted that reaction 1 does not involve the presence of greens Balls is knotted. Of course, this only applies as long as one can assume that enough grass seeds are already available everywhere. reaction

2 and 3, on the other hand, are directly dependent on a finite population of the species, i.e. of an autocatalytic nature. Then, once all rabbits or foxes are extinct, no new births can take place. Reaction 4, on the other hand, is not directly to be regarded as autocatalytic. That means z _; B * that the number of hunters per Kevier does not depend on it. how many foxes were shot. The more foxes there are, the more will be shot without necessarily bringing more hunters into the area. The complete reaction scheme is in abstract notation

- * »A (green balls come

on empty fields)

A + X ~ + Ί X (green balls are marked with

Help converted from yellow to yew)

X + Y - »- 2Y (yellow balls are marked with

Help converted from red to red)

Y- ^ B - ^ "(red balls evolve

into blue balls according to their frequency. Said that Leave the field.)

The interesting thing about the reaction scheme discussed here is that it is used for Wild oscillations can occur at the end of the game. Hence it is eminently suitable as exciting board games in the playbook is this relationship is investigated in more detail mathematically, and it is shown how, with the help of a game scheme, non-linear processes of this kind can simulate exactly. The significance of this reaction for biology is v / ird demonstrated with examples «

7417268 13917T

:

3rd example: "sense or nonsense"

How to play: "Sense or nonsense" is a combination or a Competitive game for words and sentences by one or more partners can be played. It depends on the letters rolled on the dice Put together meaningful combinations of words and sentences in the fields. However, you have to fight for the individual letter fields. One can namely "throw each other out", or after reaching a meaningful one Block sequence of certain fields. The winner is the one who can put together a meaningful message first and then include it Points is assessed. The game simulates the creation of complicated structures from different sub-units with random distributions. It explains how functionally effective structures in nature (of a complexity similar to words and sentences in our language) from random distributions emerge by evaluating them according to "meaningful" rules and developing them to perfection. Precisely this development towards perfection is demonstrated on the basis of a number of other evolutionary games in which specific sentence or tone sequences are applied through the use of certain Selection rules arise.

Preparation for the game: You use the template (Fig. 4). It contains a Distribution of letters and spaces (to delimit words) on a SxS playing field with corresponding Koordianteri numbering. In addition belongs to a pair of octahedral coordinate cubes. The distribution of the individual letters on the game template corresponds to the frequency of their occurrence in the German language. Each player receives two sets of approximately 30 (at 2 players) glass balls, each set of glass balls being a different color. (The game can also be played by three people. Then everyone gets Player two sets of only about 20 glass balls. If there are more than three players, a larger coordinate field must be selected.)

Course of the game: The game is rolled one after the other - strictly alternately. I.

The player places a ball from one of the two on the rolled field!

Color sets. If the player rolls the dice, the opponent already hits!

occupied field, he can throw the opposing ball out and through!

own substitute, provided the decision taken opposing ball even replaceable [bar is. If, on the other hand, you hit a field occupied by your own ball when rolling the dice, you can get another ball (from the first set of colors)

Place in any free space (without detracting the hit ball)

distant). As soon as a player finds a meaningful word from his j

Can combine letters, tlcnf he "blocks" the corresponding fields, j

i by playing the corresponding balls against balls of his second set of colors exchanges. You can no longer be "thrown out". You can only block if a meaningful word emerges from the assigned letter fields, z. B. "donkey", b can be further words "connected". These are allowed but are only blocked if they make sense in connection with already existing words (e.g. "You donkey", "The donkey pulls the. Cart ", but not:" be! the ", or" donkey pulls the ". however ^ 'donkey pulls cart ".) The individual words must be properly separated by spaces also fulfill the function of a joker. When combining the words and Phrases may be used as an aid with paper and pencil.

Game Completion and Scoring: The game ends when one player has all the balls and at the same time have a meaningful combination of words can. He is the winner. If all players have placed their balls without a meaningful sequence of letters, the one who changes the game wins the fewest number of letters can produce meaningful message content. The letters and spaces count as points, which are counted according to a rating system specified in the playing field.

Interpretation: At first glance, this game doesn't look like it has a scientific one Background. It will certainly be welcomed more by the German teacher than by the physics or chemistry teacher. Let's face it

But once before, we had building blocks in front of us, and let us assume a meaningful one Letter combination means that we have these building blocks in one

Macromolecule linked and folded in such a way that a small molecular '

Machine is created that catalyzes certain chemical reactions. So can

we understand that in nature, too, meaning can arise from "nonsense" - ί

provided there is a "meaningful" rating. Such had j

We already learned in Selek ^f ionsspiel in the first section. "Sensible"

is what is "advantageous" in the sense of selection theory, and "advantageous" i

is what helps one's own reproduction. j

In the game described here, one might object that words can be put together from a set of letters without having to remove them from are set in an order in advance. But in nature they fold the protein molecules from sequentially fixed chains.

A version is therefore also presented that is in this "elementary step" closer to nature: You take a game board (Fig. 2) on which the glass balls in the colors red, green, blue and yellow are sequentially in Combinations of three (three-way fields) can be arranged. The letters of the alphabet are now coded in the 64 combinations of three. There is also a code table, which in turn takes into account the number of letters in the language, by means of corresponding redundant coding. You start from a randomly rolled sequence of red, green, blue and yellow Glass balls. This initial configuration is created by thrown mutations transformed into a meaningful sentence. This game simulates that very realistically Genetic code problem. It can be varied in a number of ways, ultimately with encrypted messages between different players made out - or stored in a self-organizing information store.

7417? 6§

5. Game equipment and technical design

The complete game collection consists of a basic set of equipment that is included in each of the games is used, and from special forces that only be used in certain games. The different game sets are put together according to the modular principle, as this system allows Best meets requirements of great variability. In this way, the collection can gradually be completed and finally through expand new game combinations.

An essential aspect is the aesthetic appearance (of the design) of the game. Glass balls are predestined as play elements due to their parallel to the "glass bead game". So do the shimmering color and reflection effects that make up the aesthetic appeal of glass balls come into its own, the game board (namely the perforated board) must be made of transparent, clear plastic material. That is so also necessary, since the stencils, which are placed under the perforated plate and printed with the game divisions, can also be clearly seen have to. The stencils should be drawn with a high contrast, but must in no way impair the brilliance of the glass balls.

The game described here set of elements is supplemented by Speilanleitungen for a selection of games that can be carried out with the basic equipment z _e B ₈ in the form of index cards, the od in a game book. Like. Be classified.

This basic equipment can be expanded with the following additions:

1. A "playbook" in which the scientific basis of each Games are described in a generally understandable form. (The index cards with the various game instructions can be arranged in this booklet will).

741728 *

-'33-

2. About 15 additional specifically printed templates and the associated ones Game instructions β

3. Individual items, glass spheres, certain more transparent and fuller harbe. (In addition to the 4 mentioned colors red, green, blue and yellow; be still black and white and possibly other colors required).

4. Different types of cube (tetrahedron, cubes, octahedron, dodecahedron, Icosahedron) with surface labeling of various code systems, e.g. for the triplet combinations of the genetic code: 3 tetrahedra, the 4 faces of which bear the letters A (red), U (green), G (blue) and C (yellow). The dice must be distinguishable (e.g. black, gray and white) in order to identify the code positions reproduce exactly.

5. Special accessories, such as pierced glass balls that can be lined up, attachable cones, frames etc. for the specific identification of glass balls, playing field regions etc.

6. What's new in the game collection?

The collection of games presented here is designed in such a way that the Rules correspond to simple processes that can be observed in nature. It follows that the same idea for depicting Sohr exploiting many different scientific facts and thus a whole teaching structure can be achieved. On the other hand, these can be simple physical phenomena - apply rules for interesting parlor games as well, v / ie any other more or less arbitrarily chosen rules. You can therefore find access to the games without any prior scientific knowledge and, after one - "playing" - has gained the experience, attempting to recognize and process the underlying scientific content. “Understanding” means to a large extent “getting used to it”, which cannot be achieved with any of the known, abstract teaching aids.

7417268 13 Birr

The combination of teaching and entertainment purposes requires a technically uniform concept, which makes the logical structure of the games particularly clear. That is not with a collection of different - not with each other ', f. Consideration of standing: - To achieve games ^ because their elements are always designed according to different principles. Individual units that obey certain laws, be it atoms, molecules, polymers, cells, living beings, people or societies, must be characterized by simple symbols of the same type; useful through colored glass balls. With the help of de; Perforated plate, these can be arranged in all possible patterns and structural shapes. Only the templates have to be changed for each game, because they contain the layout of the playing field, designed according to a logical principle, for the phenomenon to be represented in the respective game. The unity of nature, yes also the unity of nature and spirit, on which Hesse's "Glasperlenspiel", the "game of games" is based, is clearly expressed in this uniform concept »The technical design proposed here offers decisive advantages over conventional board games . A game situation cannot "shake" because the glass beads are fixed in the holes. This avoids a lot of trouble, especially with children. The proposed pair combination of coordinate-throw el η offers considerable advantages for the representation of uniform α priori probabilities for a number of different number systems. This means that for numbers greater than 6 (up to 400 or any number for combinations of more than 2 dice), the more complex lottery discs or lottery drums can be dispensed with. The template principle is also cost-saving, especially when it comes to a large game set. Each new game in the collection is realized by purchasing additional templates - this also applies to all conventional games that can be easily added to this collection.

Finally, the collection introduces new types of games that can be used in of the form presented above are not yet known and also one pursue a different purpose than all previously known games. That is new

7417269 I ₉ . η

variable link between chance and law and the one that can be achieved with it
Representation of natural law reality. Eventually the high one
Claim in the representational power of the games supplemented by the execution of the game elements in an artistic-aesthetic sense. Fs \ *. I «!; O = ^! _ "Again to quote H, Hesse - a game with all the contents and values of our culture. One plays with" how, for example, in the heyday of the arts a painter may have played with the colors of his palette. "

741726 «13 0177

Claims (6)

Prof. Dr. M. Eigen Dr. Ruthild Winkler protection claims: 1. Educational and entertainment game, marked by a Base plate (14) with corner or edge edging (15) and several templates (4-13) that fit into these, as well as one over the stencils (4-13) extending, can be fitted onto the base plate (14) and are made of transparent or at least translucent Material existing cover plate (2) with grid-like arranged depressions, holes or the like. (3) and into the depressions or perforations (3) of the cover plate (2) to be used game pieces (la, Ib). 2. educational and entertainment game according to claim 1, characterized characterized in that both the base plate (14) and the Field templates (4-13) and the cover plate (2) stops, recesses, brackets or the like. (15) for their fitting A-j together are provided. 3. Educational and entertainment game according to claim I ₅ dadurr ¹ - characterized in that the game pieces are formed by glass balls (la, Ib). 4. educational and entertainment game according to claim 1, characterized in that that the game pieces (la, Ib) are provided with coupling elements for the mutual connection of several game pieces. 5. educational and entertainment game according to claim 1 to 4, characterized characterized in that the base plate (14) forms the bottom of a flat box, the side walls of which have mating surfaces (16; for the playing field templates (4 - 13) and the cover plate (2) form. 6. educational and entertainment game according to claim 1 to 5, characterized characterized in that the base plate (14) and the game stones (la, Ib) are made of magnetizable material or by permanent magnets are formed.