
barnsleyj3

    z(0) = pixel
      if real(z(n) > 0 then
        z(n+1) = (real(z(n))^2 - imag(z(n))^2 - 1) +
           i * (2*real(z((n)) * imag(z((n)))
      else
        z(n+1) = (real(z(n))^2 - imag(z(n))^2 - 1 + real(c) * real(z(n)) +
         i * (2*real(z((n)) * imag(z((n)) + imag(c) * real(z(n))

    Two parameters: real and imaginary parts of c.


Barnsley Mandelbrot/Julia Sets

(type=barnsleym1/.../j3)

Michael Barnsley has written a fascinating college-level text,
"Fractals Everywhere," on fractal geometry and its graphic applications.
In it, he applies the principle of the M and J sets to more general
functions of two complex variables.

We have incorporated three of Barnsley's examples in xmfract. Their
appearance suggests polarized-light microphotographs of minerals, with
patterns that are less organic and more crystalline than those of the M/J
sets. Each example has both a "Mandelbrot" and a "Julia" type. Toggle
between them using the spacebar.

The parameters have the same meaning as they do for the "regular"
Mandelbrot and Julia. For types M1, M2, and M3, they are used to "warp"
the image by setting the initial value of Z. For the types J1 through J3,
they are the values of C in the generating formulas.

Be sure to try the <O>rbit function while plotting these types.

