Bugs #14

Bugs Fractal 88

There are several pictures on my hard drive that are queued up to post here. The plan was to introduce the bug formula, provide some nerdy math descriptions and examples, then start posting the more artistic images. I am done with the nerd stuff, and then noticed a problem with that plan; most of the images I have are based on another version of the bug formula. I won’t keep you in suspense. You may have guessed the other variation. I added a letter to the name to keep track of which part is gets modified.

bugI(x+yi) = x + a * sin(y/a)i \\ bugR(x+yi) = a*sin(x/a) + yi

As a quick recap, the bug formula is combined with the usual z^2+c, and the images are generated in a typical escape-time fashion. There are two variations of the combined formula, depending on who goes first.

(bugX(z))^2+c \\ bugX(z^2+c)

Most of the pictures here use the second “bug last” variant.

The pictures of the last two weeks have been based on bugI(). Today’s picture is based on bugR(), with a = 1.5.

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