Category: Escape-time Fractal

Developed by Clifford A. Pickover, this is another derivative of the Julia sets by adding a function (here: sine) to the Julia set formula.

> restart:

> julfn_zsqrd:=proc(x, y)
>    # Based on a Maple V algorithm taken from the book 
>    # 'Maple V - Programming Guide' by M.B. Monagan, 
>    # K.O. Geddes, G. Labahn and S. Vorkoetter, 
>    # Springer Verlag, modified by John Oprea
>    # modification of initialization and iteration by Alexander F. Walz
>    # May 26, 1996
>    local c, z, m;
>    c := evalf(-0.5 + 0.5*I);
>    z := evalf(x + y*I);
>    for m from 0 to 30 while abs(z) < 3 do
>       z := sin(z) + z^2 + c;
>    od;
>    m
> end:

> plot3d(0, -1.91 .. 1.37, -1.24 ..1.21, style=patchnogrid, 
>    orientation=[-90,0], grid=[250, 250], scaling=constrained, 
>    color=julfn_zsqrd);

MAPLE V FRACTALS JULFN+ZSQRD #1.01 current as of May 18, 1999
Author: Alexander F. Walz, alexander.f.walz@t-online.de
Original file location: http://www.math.utsa.edu/mirrors/maple/mfrjulfn.htm