**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*