Mike,
I got the same images for both the Wikipedia and yozh formulas. I do see a slight difference in the Wikipedia formula I used and yours.
Mine: ;cz = cos(z * pi / 2); ;sz = sin(z * pi / 2); ;z = (z / 2) * cz * cz + sz * sz * (3 * z + 1);
Yours: hlfpi = PI * 0.5 Zhlfpi = z * hlfpi z = 0.5 * ( z * sqr(cos(Zhlfpi)) + (3 * z + 1) * sqr(sin(Zhlfpi)))
Shouldn't that 0.5 apply only to the first term, not the whole equation like:
z = (0.5 * z * sqr(cos(Zhlfpi)) + (3 * z + 1) * sqr(sin(Zhlfpi)))
The wiki page referred to by David uses (3 * z + 1) / 2. With the statement that this yields smaller values for the stopping time without changing the overall dynamics of the process. Clearly, it generates a different image. Using your version makes sense to me.
If anyone would like, I can make an exploration page for this fractal with images and a forum discussion area. I have something like that setup on the Fracton website for some other fractals already. It would only take a few hours to set it up.
Sure, that sounds good. collatz-potential { Jonathan Osuch reset=2050 type=formula formulafile=collatz.frm formulaname=Collatz center-mag=0.498123/-0.00125209/9.180077 float=y maxiter=1000 inside=0 potential=256/100/100 colors=000_2t<4>b1qc1qd0p<14>n0fo0ep0e<9>u3Yu3Xv3W<10>y8Oy9NzAM<14>zJCzK\ BzLBzMAzMA<6>xS6wT5wT5wU5<5>tZ2t_2s_2s`2ra1<16>hm0gn0fn0eo0ep0<9>Yu3Xu3W\ v3<10>Oy8Ny9MzA<14>CzJBzKBzLAzMAzM<6>6xS5wT5wT5wU<5>2tZ2t_2s_2s`1ra<16>0\ hm0gn0fn0eo0ep<9>3Yu3Xu3Wv<10>8Oy9NyAMz<14>JCzKBzLBzMAzMAz<6>S6xT5wT5wU5\ w<5>Z2t } frm:Collatz [float=yes]{ ; Collatz fractal z = pixel hlfpi = PI * 0.5 : Zhlfpi = z * hlfpi z = 0.5 * z * sqr(cos(Zhlfpi)) + (3 * z + 1) * sqr(sin(Zhlfpi)) |z| < 100 } Jonathan