Polyplots 8 – Posters

As a poster or wallpaper

That’s right, I made posters. And not just one or two, but twenty!

I’ve made 20 distinct polyplot posters (as of this writing) that are for sale on RedBubble. Some designs are also available on other mediums, like a clock or a t-shirt or notebook or canvas or etc. (you: “I’ll buy the one on the ‘etc.’ medium!”) I’ve tried this sort of thing before through deviantart but that didn’t pan out. Also, that site has gone through a redesign, which, like all websites that do a redesign these days for some inane reason, makes it much worse. But anyway, here they are!

I’ve done a few of these images before, but to make them larger for a poster, I just needed to increase the degree while keeping the coefficients roughly the same. But I did discover that I don’t always get the same output image while increasing the degree. In fact, they only show up for certain degrees. For instance, using the coefficients used to make the Lacey Orb design:

Number shown is the degree, all coefficients for all degrees were either -1, 1 for the odd coefficients (a, c, e, …) and -75i, 75i for the even coefficients (b, d, f, …), all centered on -0.5+0.866i. There aren’t actually any roots in images 0 thru 4; 7 and 8 have one each in their bottom right corners

The central orb structure only shows up for degrees 5, 6, 11, 12, 17, 18, 23 and 24. But for enough resolution for a large poster, I had to go higher than degree 24. So I ran code at this spot for degree 26 (taking 4 times longer than degree 24) and didn’t see the central orb – this is when I discovered that such things will only show for certain degrees.

Taking the pattern above, I followed its continuation and guessed it would show up again at degree 29 and 30. I ran it at degree 30 and sure enough, it showed up! This also had enough resolution for a poster; the next step up (degree 35) would likely take me some five days to render!

I haven’t yet figured out why certain structures will only appear with certain degrees, but it’s both annoying (time wise) and fascinating (math wise). I have noted that the pattern of which degrees contain a certain thing change based on the location, so the pattern above only works for certain areas (as far as I can tell right now). Using the same conditions as the above, but now centered at  -0.707+0.707i instead, the central structure at that location only shows up for degrees 7, 8, 15, 16, 23 and 24:

But I digress; take a look at these things for sale today!

‹ Giraffes

Radio Trees ›

Tagged with: fractal, math, polynomial, PolyPlots, posters
Posted in PolyPlots