Friday, 3 April 2009

Trigonometric Julia Set Images

The usual Julia Set images are generated by repeatedly running the formula z→ z² + c.
But there are other things that we can do to generate variations, like trying different powers of z.
One of the cooler variations is to replace the usual Julia formula with z c× f(z), where f(z) is a trig function. This was the method I used to create the (TAN-based) cellular and (SIN-based) circley fractals in the 1st March and 9th February blog posts.

Thanks to Pythagoras' Theorem, trig functions include terms, so there's a certain amount of crossover between the "conventional" and "sine" Julia sets.

Web-wise, priority seems to go to Paul Bourke and Tim Meehan for putting up a webpage on "Julia set of sin(z)" nearly ten years ago.

For those who want to see more, there are some more "sine Julia" and other "trig Julia" images on the website on three new pages, here, here and here. The third page shows how more complex and more strongly repeating versions of the more familiar Julia Set images (example above) appear within the "sine Julia" parameter set.

Some of the pictures are cool.

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