On Friday 15 October 2004 9:32 pm, david lowenstein wrote:

I wonder if the Sierpinski formula can be generalized? -david

Here is a formula for the Sierpinski type that I had generalized for Jon Horner and FRAC'Cetera. I did update it to use the newer if-then and ismand instructions. Note that this type is already a Julia set. base { reset=2003 type=formula formulafile=sierpnsk.frm formulaname=Sierpinski_gen ismand=n function=ident/ident center-mag=0/0/0.6666667 params=0/0/0/1/0.5/0 float=y inside=0 } frm:Sierpinski_gen {; Jonathan Osuch if (ismand) z = (0,0), c = pixel else z = pixel, c = p1 endif flp = flip(p2) change = real(p3) bailout = imag(p3) if (bailout == 0) bailout = 127 endif : oldx = fn2(real(z)) oldy = fn1(imag(z)) z = z + z + c if (oldy > change) z = z - p2 elseif (oldx > change) z = z - flp endif |z| <= bailout } Jonathan