Back to Vagrancy

Now that I'm out of ZU (my old employment), I'm back to vagrancy. So I'll have a bit more time for my blog.  My first thing will be to redo all the links that use SVG files.  I will probably just host my images on but I'll do it when I have access to a real computer not my 7" tablet.  We'll have to see if I extend the scope of my blog to include more than just polygons to some visualizations like my "Weeping Willow" figure that depicts the hailstone function.  I particularly like the meaningful drooping branches that happen to be composed of numbers that are multiples of three.  I was probably thinking about using that resource to teach about CSS but it's current form is too complex.  I'm not sure if I can simplify the example into something that would work well with novices.

I guess since I can't fix the images yet, I'm stuck with writing about these less polygon things...  Unless I can easily link it to polygoncraze...…

Opacity Changes

I really like this small change. I wasn't expecting such a big difference. I was aiming to promote the octagram called the Star of Lakshmi or khatam sulayman, which is two overlapping squares following the recent descending pentagons had two overlapping pentagons. I switched back to emphasizing the square rather than the triangles and ended up with this above pattern. I quite like the details in this pattern. Probably, it doesn't actually benefit that much from the animation. Or perhaps I need to work on a different animation...

Descending Squares

Unlike normal, I was able to deliver the square version of the descending pentagons quickly. There was no math to figure out. although there was one interesting choice that I looked into. The choice was to place the 45 triangles to be touching the previous square rather than the corner square. I guess it's simply a preference about complexity. I like both. The first version is a simple analogue of the descending pentagons--actually it was the original doodle on my boogie board. I find the boogie board is a great exploratory tool because of it's impermanence. Somehow it helps me focus on process rather than product. The version of the boogie board I have doesn't save any of your work and there is no erase so you are stuck with any mistakes unless you erase the entire drawing. So I am tasked with focusing on the internalizing any thing that I do that I think is important. Perhaps this is a bit of a throw back to all the time I spent with chalk and blackboards. Regardle…

Descending Pentagon

You have to reload this page to see the animation ...perhaps I should put it on a bit of a repeat.  It took a surprising amount of high school math to unravel how to make this.  I guess I could have been content with just eyeballing it but that seems to take all the challenge away plus it makes it more difficult to augment later. Perhaps I should have used a better tool than Excel: maybe Geometer's Sketchpad.  Next time.  Perhaps I'll put up the square version of this pattern when I get the time.   Essentially, it's a snazzy version of starting with a pentagon and using the sides midpoints to make a slightly smaller pentagon and descending forever (or in this case 12 levels?).  The snazziness is was the time consuming part.  Computing the lighter bands took a bit of effort--more of a stamina thing rather than a difficult thing.

Octagonal flowers

This pattern has a few cute things: a right and left handed version of the flower and some structures that seem a little out of place. The green flower is the left and the purple is the right. What I find more interesting is the way the 4 octagons behave between the flowers--there is a diagonal slit between them that alternates its direction.  The pentagons are just decorative but they make the white space more interesting.

Quilt and wallpaper

I was going to try to get this into last month but alas February only has 28 days this year. here is a toned down copy that works for wallpaper wall (colour), wall (blue), and wall (sepia). I was a bit lazy using a tool to crop it so it's in pdf rather than svg...but my MacBook pro accepts it as my desktop background so I didn't pursue it.

from Pentagons to Heptagons

I needed to do a modification to go from pentagons to heptagons: add a square between the triangles. Without the square the heptagons would intersect. I wonder how close there pentagons are....