# FRACTALS BY VARYFRAC

(You may click on each of the pictures on this page to get a larger version)

## Fractal With Equation z = c -.3*z^4+ 1.3*z^2

MANDELBROT-QUARTIC

## Fractal With Equation z = c + 1/((z-1)(z-i))

CHAOS

In these factals, we use iterative equations z = c + f(z) for various functions f. The iterations may result in converging or diverging values of z. Scanning the screen as if it were the complex plane, we use the iterative equation a fixed number of times to compute the values of z. We then color the "points" (pixels) according to various convergence criteria. For example, we color a point one color if the values of z converge, another color if they oscillate between two values, another color if they oscillate among three values, etc..., and still another color if they become unbounded. This method produces "interior" (non-black) colors in Mandelbrot sets and other fractals.

## Fractal With Equation z = c + -1.5z^2 + 2.5z^4

`z= c + z^4    z = c + z^4 + .95/z    z = z^4 + 1.05/z`