Tag Archives: julia set

Coloring the Julia set

The Julia set of a function f(z) in the complex plane has all points z that remain finite upon iterations of the function. In the last posts I have used expanding functions to get fractal images from iteration, as discussed … Continue reading

Posted in Fractals, Self-similarity, Uncategorized | Tagged , , , , , | Leave a comment

Complex function iteration: Further results and a puzzle

I used the method of the post “Fractal surprise from complex function iteration” for the function where c is a constant. To get a better image I now use dark blue for all numbers z that grow without limit in … Continue reading

Posted in Self-similarity | Tagged , , , , | Leave a comment

Another surprise from complex function iteration

Playing around with my program I found a remarkable result. I used the function f(z)=z*z*z*z+z*z+0.000002 in the iteration. Because of the leading 4th power this multiplies the complex phase by four for large z. Thus the compensation is minus three … Continue reading

Posted in Self-similarity | Tagged , , , | Leave a comment

Fractal surprise from complex function iteration: The movie

The movie shows the images as discussed int the earlier post “Fractal surprise from complex function iteration” for a decreasing value of the constant c. The program of the last post creates the movie frames. The movie begins with c=0.4 … Continue reading

Posted in Self-similarity | Tagged , , , , , | 1 Comment

Fractal surprise from complex function iteration

Recently I got the inexpensive Dover reprint of Clifford A. Pickover’s book “Computers, Patterns, Chaos and Beauty”. Part of it extends topics presented in “The Armchair Universe” by Dewdney. And there are other interesting ideas in Pickover’s book. Get it, … Continue reading

Posted in Self-similarity | Tagged , , , , | Leave a comment