Fractals of the Week | Come Halley or High Water!

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This week, I’ve a few pieces done using the math of Edmund Halley, of comet fame, whose method for finding square roots bears some similarity to Newton’s method, but which can produce images of wholly different character. A few years back, I found such math challenging to work with, but with time I’m increasingly satisfied with the results. Here are two of them:


An alien spider at the center of its web? Maybe. It’s currently untitled, and this piece like the next does not make use of quasi-3d orbit trap settings. Both of these use only the limit set, brought out by the color mapping of each piece to best effect. Well, best out of a series of attempts using a coloring randomizer, and selected from those that didn’t make the cut as either too pixelated, or too garish. Many of you are aware that I tend to avoid colors that one might find on a psychedelic black light poster from the 1970s. That is, unless requested to do otherwise for commission work.


This one is a bit more anthropomorphic, perhaps suggesting a face, or a badly drawn ancient medical diagram of an absurdly over-muscled human figure. I was less displeased with the coloring for this one, and I think I’ll keep it in my archives. I’m currently updating the file addresses of all my pieces, from the very first set of image folders to the very most recent. It’s coming along quickly, and perhaps once finished, I’ll have time to improve on this piece, as I intend to do for my more interesting early pieces, themselves far too small to make good prints, but otherwise decent.

It pays to revisit old apps with not-so-old ideas. Now then, I have cats to attend to. May you all have a beautiful time of what remains of the week, and I’ll see you sometime.

Tf. Tk. Tts.

All JPEG, PNG & GIF images in this post are original works by the author, created via a variety of apps and unless otherwise stated are copyright 2016 by Troy Loy. I hereby permit the free, noncommercial use of these images, with proper attribution or a link back to the original source. Thank you!

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