John Burridge

One of my hobbies is playing around with different types of tilings.  Mostly I like to play around with Penrose Kites and Darts.  I also like to try to fit stars into regular patterns.  The most recent exploration that I've done comes from Daud Sutton's "Islamic Design," where he talks about making a grid out of right triangles, and then placing regular polygons and other shapes onto the edges and corners of the triangles.  In the case that I was interested in, he used five-pointed stars.  

Getting the stars down on the triangles was simple enough, but it took me a lot of wiggling to get the nine kite-shapes at the top and bottom of the design to look symmetric and not smooshed.

I'll have to see what sorts of patterns will result from right-triangles which form squares instead of hexagons.

A couple of weeks ago, I read about a technique for putting odd-numbered polygons and stars together.  Start with a figure, duplicate and reflect it, then make the two closest points touch.  Skip a point on ether side of the touching point, and place a reflected duplicate there, too.  This will make a repeating line, which you can put together into a mesh.  I tried it with 5-, 7-, and 9-stars; the 7-stars were the most aesthetic, so I put together some interwoven 7-stars into a larger interwoven pattern.

Whats fun about this technique is that it allows one to break away from patterns that are hexagon- or square-based. 

It's that pause during the year before it seems like everything happens all at once.  Thanksgiving will hit, I'll need to figure out some sort of holiday craft gift, start production, and mail out items soon.  And set up a Winter Solstice Lights Spiral.  While trying to write, going to work, and other everyday tasks.  Somewhere in all of this we want to send out holiday cards, too.  

We've made some fairly creative holiday cards in the past; I think "Smokey Knew He Could Save Christmas" was my favorite.  A few years ago, there was an abortive attempt to have us riding the notes in a music score for "Jingle Bells," but Mark thought it was "too gay," and we've devolved to generic portraits.   Perhaps this year's card will be "Merry and Tired."  

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The other day I finished "wiggling tiles," as I liked to put it, and came up with a tile pattern using pentagons.  

I was pleased with the effect, but I had a suspicion that I'd done something similar.  Sure enough, as I was going through my photo collection to try to find pictures for a family 2023 calendar, I ran across a design I'd done last spring that was virtually identical.

And looking more closely, this is essentially a variation of interlocking circles within a hexagonal array, which I did a variation of last November.  I suppose there's only so many ways one can have repeating infinite tiles using pentagons, and it involves arranging them around hexagons.  

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I'm trying to decide if Twitter imploding is a good thing or a bad thing.  

The other day I revisited the interlaced septagram.  I wanted to make the areas between the rays more even, and I ended up doing a double-interlace.

This design suggests to me that it could work as a a meditation guide; I see several skewed perspectives in it, and the curves have a feel of water and bridges to them.  

Perhaps I'll stare at it before going to bed and see if any interesting dreams appear.

The other week I saw an interweave design entwined around the letter H in a medieaval manuscript.  I liked the combination of interlocked squares and and vesica piscis (it turns out the vesica piscis is not a true one).  So I set out to make something similar.  

The other day I saw a design out of an old Arabian dictionary.  It was two interlocking squares, joined together by arcs into one continuous line.  It looked like something I could copy with a straight edge and compass, and in fairly quick order, I was able to work out the underlying geometry.

It's been a while since I photographed the planets.  Saturday, we had a break in the weather:  the morning sky was clear and cold, which meant that Venus, the Moon and Mars were visible in the pre-dawn sky.  Venus is approaching its greatest brilliance, in a few days it should be visible during the day.  The Moon was three days before being new, and rose something like 5 AM.   Mars was dim compared to the Moon and Venus.

All three objects were fairly low in the sky, which necessitated crossing the street with camera and tripod. After contending with some awkwardly placed power lines, I managed to frame the sky over the eaves of neighbors' houses.  It would have been nice to have a tree's silhouette in the photo, but the rooflines looked like mountains or possibly pyramids.  

After a quick jaunt to the store for tea, I set up the camera and tripod in the backyard against the arbor vita trees, focused on the fountain, and waited for the hummingbirds to appear.  Of course, the first hummingbird to appear came while I was futzing with the tripod and I only managed a blurry photo of it flying off.  I finished set-up.  I felt a little like some early twentieth century British Naturalist, as I had set up a small end table, chair and cushion, and had wrapped myself in faux leopard skin fleecy blanket.  

As I was sipping my rapidly cooling tea, a fierce humming signaled the sudden arrival of a bright red hummingbird.  It peered at me down its long and pointy beak, and, as I Tweeted later, I was pretty sure it was challenging me to a duel over ownership of the fountain ("Hello.  I am a hummingbird.  This is my fountain.  Prepare to die.")  

The light meter on the camera helped me to gauge the sun's progress, as I would have to adjust the shutter speed to compensate for the increase in light.   When the hummingbirds came to the fountain I was mostly ready.  I took many photos, fiddled with fine-tuning the camera's focus, and managed a number of good shots and one excellent one (the first one).  

By the time my tea had defrosted the glass top of the end table, it was too cold to drink.  

I spent the rest of the morning processing photos, and then it was time to go to my folks for a socially distanced celebration of my Dad's birthday.  We brought gluten-free cupcakes as a alternative to a socially closer birthday cake with candles.  Mark and I (okay, mostly Mark) had painted a sign for his garage, which he's converted into a combination wood shop, gym, and indoor dog play area.  It looked a little like a medieval manuscript, with the H in his name outlined and a medieval dog at the bottom.  I'm pretty sure he liked it, or at least appreciated it.  His ginormous German Shepherd and Aoife played together; we played "Apples to Apples."  

Then it was time to run home and feed the cats.  

The evening wound up with the finishing touches on a the latest geometric Math Art.  

If Saturday was the Day of Producing Art, Sunday was the day of Relative Sloth.  

 

 

 

The latest adventure in not writing playing with graphics is a stellated dodecahedron.  Someone posted a picture of a marble floor mosaic from the Basilica of St Mark.  I'd seen it before, and I decided that I could probably copy it.  So I dug out my compass and ruler, constructed a pentagram, and went forward from there.

I switched to InkScape once I saw how the design is basically pentagonal rotations.

and added some etching lines.

 

I'm not sure which version works the best.  I like the etching lines--especially when the design is viewed from a distance, but I think the solid colors work better because the optical illusion of the triangle placement makes it look like I used more than six shades of grey.  

 I've been fiddling with the Three Hares icon.

The trickiest part has been choosing a color combination that doesn't make the hares' ears disappear into the pattern.  

On the creative front, I've come up with some holiday patterns in InkScape to use as backgrounds for when I'm telecommuting to work or holiday events.  I started with a square, then I duplicated them so I had five, then rotated them 72 degrees and grouped them into star patterns.  The star groups are either pointed upward or downward.  

Pentagonal designs tend to fall into two categories:  five or ten rays radiating from a central point, or rings of alternating units.  

The first design I came up with starts with a upward pointing star group; each of its five edges are joined with the edges of a downward pointing star group, which forms a ring around the center; each of the ten free edges on the downward pointing star groups are joined with an upward star, forming another ring, and the whole design keeps repeating that way.  What's interesting to me is way almond-shaped gaps open up in the network of star groups.

For the second design I wanted more complete circles (actually bevelled decagons or icosagons).  The decagons can only hold three star groups at most, with the result that a decagon can only overlap with at most only two other decagons.   In addition to the almond-shaped gaps, packing the decagons together creates a boat- or T-shaped gap and also a star-shaped gap in the arrangement of star groups--I arranged star groups in a way that would favor the creation of complete decagons and star gaps. 

The third design is the second one, only zoomed out a little.  Since this is all done with pentagonal symmetry, the designs end up looking like zilij or Penrose tilings.  I suppose I should go back into InkScape and change the colors; red and green are traditional for the winter holidays, but a number of people have commented that the contrasting hues make them dizzy.

 I thought that I would try to make a seasonal design for the Ides of Autumn.  I was trying for something based on a crescent moon, but when I put in a second notch in the crescent, the result looked like something Batman would use to fight crime.  Or a sigil for Klingon Pagans.

I tried a few different designs, but they all looked like something for a Sapphic Pagan Metal Band called "Vagina Dentata."

I finally ended up with some wreath shapes that don't look too lethal.  

This is my take on Crockett Johnson's Square Root of 2.  (Apparently, not only did he write Harold and the Purple Crayon, but he was interested in math art.)


I wanted to see how different numbers and different scales would work out.  This is an exploration of the square root of 4, 9 and 16.  If you want to find the square of a number n, make a semicircle of diameter n+1; the length of the perpendicular from n to where it meets the arc of the semicircle will be the square root of n.  Somehow this is related to the Pythagorean Theorem, but I haven't quite figured that part out.

Lately, I've been wiggling shapes together to try to make interesting tessellations.


I have to say every time I make a foray into this sort of design, I have to stop an appreciate 500 year old tile artists who managed to work out these patterns without computer assisted drawing (although, they do fudge shapes away from strict geometric polygons).


What typically happens is that I start in on a design that clicks into place on a local level but once I start to extend the repeats out -- or try rotating the whole pattern 120 degrees instead of 90 -- there's a fractional repeat that starts adding additional recursive shapes.


Theoretically, one could get around the difficulties of using both squares and triangles by designing a pattern with twelve-fold symmetry).


Looking at books on design, it seems the best strategy is to arrange squares and triangles and stars along radial guidelines and then wait for patterns to snap (mostly) into place.


Five-fold symmetry, as I've noted before, is very hard to tessalate unless one folds the two-dimensions of the workspace into three dimensions.  My intuition tells me that folding a pattern of ten stars into a regularly repeating pattern is somehow part of the same property of our universe that means you have to fold sound somehow if you want to make seven octaves and twelve fifths a unison.

Thursday, Aug 3

Today was a sandcastle day!  I went out to the beach around 9:30 with my compass, yardstick, and small bag of supplies.  Low tide wouldn't be for a couple of hours, and nary an umbrella could be seen on the wide, flat shore stretching away north and south.  The day stretched forward like the smooth sands around me.

First I made a net of circles--a tessellation of six circles around a seventh in the center.   It's a relaxing pattern that let me get a feel for how the compass would respond in the sand.  I continued the net out and then highlighted various circle sections to add some visual variety.

Then I made a simple spiral labyrinth; next a bird constructed of repeated circles on a line.  The bird came out vaguely flamingo-like, so I added a small hedgehog next to it.  By this time I noticed that I needed to hold the apex of the compass in my palm if I wanted to avoid having the rubber bands in the hinge flex and make different shaped circles.

The occasional jogger and one beach comber with a metal detector came by.  A woman asked me if it would be OK for her to photograph my labyrinth.  Later, a woman and her child stopped by; we tried to interest the child in walking the labyrinth, but she only wanted to watch adults walk the spirals.

A group of four teen boys set up the first umbrella; they had some musical device with them which was slightly annoying, but easy to ignore.   Mostly they sat in beach chairs looking out over the waves.

It was time to design the sand castle.  I wanted it to be more historical than random.  I drew a very large circle, then two interlocking squares for placement of eight outer curtain wall towers.  Then a smaller circle and square arrangement within for the inner curtain and central keep.  I suppose that historically, this would make my castle a late fourteenth century castle, with towers in corners supporting outlying towers from cannon fire.

A retired engineer came up to see what I was doing, and we had a talk about castles and Oregon -- it turned out he had done some consulting on structures' abilities to withstand waves at various points along the Oregon coast and sort of knew Corvallis (where OSU has a wave lab).

I returned to construction.  One of the supplies was a simple tower sand-mold, so I placed some of the towers.  The resulting towers were simple, but towering enough.  Sand from the excavated moat was piled into the center for the keep.  Occasionally I would pour water onto the pile and pound it to consolidate the sand into a mass I would be able to carve.  In the back of my head, I recalled that sand sculptors said they started at the top of the sculpture and worked their way down.  The tower-mold helped a lot, and by happy coincidence, seven in a row was the length of the inner curtain square.

At some point, my legs were cramping from all of the crouching, digging, and inscribing in the sand.  The beach started to fill up.  I wondered where the Dwyers were.  More people joined the four teens, and I saw that they were Canadians.  Sure enough, Marc appeared, said hello, and then a bunch of them walked toward the ocean with snorkels.

Later, the Canadians, spurred on by Marc, broke out shovels and pails and in no time had two large mounds built.  A few towers dotted the mounds, built from the deep trenches.  Another family on the other side of me also had shovels, which they used to make a kind of sea wall between the now incoming tide and their encampment of beach umbrellas, towels, and chairs.

On the other side of the seawall folks, I saw the Dwyer camp.  I saw Mark and The Child and walked over to him and sang a re-worked song from Avenue Q, "Oh, I wish you could meet my boyfriend / but you can't, 'cause he lives in Canada!"

"Oh," said Mark when he saw Marc.  "I spoke with him the other day; he's just friendly -- I don't know what my family is talking about."  Mark then went on to point out to me that my back was beginning to sunburn.  Twice.

I gave Mark and The Child a tour of the sand-works so far. The Child seemed nonplussed, and was more interested in swimming.  They added a few towers to the outer curtain and then left.

Finally, the castle was finished, or at least as finished as I wanted it to be.  I worked on another design, which started out like a racetrack and then started to look vaguely sexual, so I added more half-arcs to make it less like a yoni-lingam and more like interlocked arcs, which then threatened to turn into a swastika, so I stopped and took all my tools to the Dwyer encampment.

The tide would be splashing over the sand soon, and I was tired from all of the construction.   I'd noticed a small boy running back and forth and he finally built up enough courage to ask me if I had done all the drawings, and how (at first I thought he was one of those monsters who stomps on unattended castles).

"Hold, on," I said.  "Wait right there; I'll be right back."

He rooted himself to the spot, and I returned with the compass and ruler.  I explained how the compass opened and closed and let him have a go at it.

"Hold it and walk backward," I said when he jammed the compass into the sand and couldn't move it farther.  He made a circle and handed the compass back.

A woman, presumably his mother, hovered on the edge of our conversation, nodded her head and made a calculated grimace which I interpreted to mean "OK, this middle-aged, bearded Oregonian appears to be not summoning demons" and then wandered away when all we were talking about was geometry.

"Circles like to make triangles and hexagons," I said.  "What's your favorite shape?"

This seemed to confuse him and he said he pretty much liked all shapes, but that squares were cool.  So I used the compass and ruler to make a square in a circle, then extended the diagonals to draw a second square around the circle, and went on to reconstruct the plan of the castle.

He watched, enraptured.  I was glad to show it to him, and wished that The Child shared the interest - but he doesn't, and I suppose he makes up for it by enjoying Monty Python with me.

Later on, the tide came in.  At first the lapping waves cascaded into the moat, and I thought the castle would stand for a while.  But, I'd left an opening in the walls for the gate and the water poured through it much more vigorously than I'd imagined, and the castle fell to the waves within minutes.

---

That evening, with some amusement, we realized the Canadians were renting a house directly across the street from ours.  This of course prompted more renditions of "I wish you could meet my boyfriend."

Dinner was casual.  Afterward the kids went to the boardwalk, and The Child had fun smacking into mirrors in a mirror maze.

I want to be in the local March for Science in April, and I'm thinking about a poster.

I started working on a Jupiter-based one with the thought that Galileo was forced to recant what he'd seen in the telescope (and I was so intent on the layout that I spelled science "sciece").  But I'd gotten the story mixed up:  he hadn't been forced to recant that he'd seen  moons orbiting around Jupiter. Instead, he'd recanted that the Earth orbited around the sun in a heliocentric system.  His inquisition was possibly brought on as a result of churchmen seeing themselves cast as the Simpleton in Galileo's "Dialogue" between a Simpleton, a Student and a Sage.  So my design with a telescope  and Jupiter wasn't so good.

Then I thought that I'd try to make a poster about the Burning of the Library of Alexandria, except that it might not have been burnt down so much as defunded.  There are parallels between defunding the Library and defunding NOAA, but I'm not sure how to make that a poster, much less a poster with cool-looking flames on it.

I wish we still had the Art Nouveau and Art Deco gods and goddesses of industry:  the burly men holding lightning bolts and gears, and women with wind-swept hair holding wheat and fish.  Maybe I could fashion an image of science and science funding with that style.  This line of thinking led me to images of industry and recruitment posters from the two world wars.

From there I recalled the Homeric story of how Hephaestus--or Vulcan, to use his Roman name--made a shield for Achilles, showing the good life.  Would my March for Science poster show the lame god at his forge, fashioning the circular shield and showing tools of science along the rings?  I could have flames curling out of the forge!

But the martial nature of the image --a war poem about the forging of tools of war --bothered me.  I'm marching for science, and peaceful applications of science.  Should the story be retold, with a shield of war, a shield of commerce, and a shield for the rest of us?  Maybe I should turn to the goddess Athena -- didn't she create a mechanical owl?  Oh, wait, no, that was the original "Clash of the Titans."

I was coming to the conclusion that I didn't have a good narrative, something that would make a good visual image, like Prometheus bound.  Er...  Albert Einstein working out relativity?  Richard Feynman's quantum mechanics notation?  Robert Oppenheimer and the work on the atomic bomb?  Mr. Spock deciphering glyphs on an alien obelisk?  Commander Data learning the Vulcan nerve pinch?  Frankenstein and his monster?

I think it's a misstep to focus on one specific scientist, not because I don't want to celebrate particular scientist, but because I'm marching to show that I think science should be funded on a national level and data and the scientific interpretation of data should inform long-term national policy.

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I went to the library to try to find mythical figures in science which would suggest a strong graphic to use on a poster.  There were a lot of books on the science of mythology, or the science behind magical beliefs, or the "Mythbusters" series.  But not a lot on the mythic meaning of science, or stories we share as a culture about how to do science.

There are some misconceptions about how science works:  the apple falling on Newton's head, or the idea of a rebel scientist working alone to make a breakthrough.  But these aren't myths in the sense of a story or symbol that explains.

I'm coming to the conclusion that science -- or at least science funding -- doesn't have gods and goddesses.  We have a toolkit:  measurement, rigorous observation, deductive reasoning, and disproving the null hypothesis.  And Bunsen burners.

So how do we keep our signs and march from eliciting the response, "So what?  The elites are crying because their toys got taken away," or "You guys sure spent a lot of money to put a remote control dune buggy on Mars."

"Science is hard," plays back into the idea of elites with toys, too.  Why is it that athlete-elites command so much respect, and science-elites less so?  It takes athletes a lot of practice to get to the Olympics, and some experiments can take as much time and effort, but do we have cities bidding against each other for "science Olympics"?

---

In the original Disney movie, Tron, there's a scene between Dr. Walter Gibbs, the original founder of a corporation, and Ed Dillinger, its current CEO.  "User requests are what computing is about," says Dr, Gibbs.  "Making money is what computing is about," says Dillinger.

Perhaps I should adopt a different narrative:  funding science will avoid a future Midas story, where plutocrats turn everything they touch into robots; a story not with serfs serving plutocrats, but with drones serving modern-day Borg-ias.  Maybe this isn't so much about de-funding science so much as it is about keeping a serf class uneducated, or industry unregulated.

Somewhere in the back of my mind was an early American quote about a well educated public. I did some searching and found this quote from Thomas Jefferson: 

"The value of science to a republican people, the security it gives to liberty by enlightening the minds of its citizens, the protection it affords against foreign power, the virtue it inculcates, the just emulation of the distinction it confers on nations foremost in it; in short, its identification with power, morals, order and happiness (which merits to it premiums of encouragement rather than repressive taxes), are considerations [that should] always [be] present and [bear] with their just weight." --Thomas Jefferson: On the Book Duty, 1821.

and also

"The most effectual means of preventing [the perversion of power into tyranny are] to illuminate, as far as practicable, the minds of the people at large, and more especially to give them knowledge of those facts which history exhibits, that possessed thereby of the experience of other ages and countries, they may be enabled to know ambition under all its shapes, and prompt to exert their natural powers to defeat its purposes." --Thomas Jefferson: Diffusion of Knowledge Bill, 1779. FE 2:221, Papers 2:526

At this point, it seems like I need Lady Liberty arm-in-arm with the all Nine Muses...  And to think all this started with me wanting to make a sign to carry on a protest march.

Since the dream that I had the other night about randomly shifting floors, I've been trying to figure out how one would use rotating gears to create a random path.  In the dream, there were interlocking circular path disks, six set around a central seventh one in a larger disk, repeated again.

Here's the latest design I've been working on.  If I were the sort of person that got tattooed, I might get this.  I might make it a T-shirt design. If I'm feeling extra creative, I might try flipping it so that the snake's head is at the bottom of the triangular knot, which might give the design a little more dynamism.

The school where The Child goes to wanted to make some mallets with the school's R logo on them.   Someone much cleverer than me in the ways of woodworking made the mallets, and figured out a way to use blank tiles of white oak to put the mallet together.







I had to convert the pixelated logo into a vector drawing of the logo in InkScape, which I surrounded with boxes the size of the wood tiles.
When I got to the Maker Space, I laid the side of a cardboard cereal box into the laser cutter, and had it etch the design onto a cardboard cereal box so I'd know where to put the tiles.