Fractal of the Day (FotD) by Jim Muth

FOTD -- July 23, 2009 (Rating 6)

Fractal visionaries and enthusiasts:

Today's image is another venture into the multi-dimensional world created by the DivideJulibrot formula. Apparently I have already posted two previous versions of this formula, which are all slightly different, but hopefully will produce the same images from the same parameters. Even now however, I see a way to make the formula a bit faster, so I cannot guarantee that the version included in today's parameter file will be the final version.

I named the image "Water Lilies" when it reminded me of water lily leaves floating on a quiet tropical pond. Actually, the image is very closely related to the fractal trees I occasionally post.

The rating of a 6 indicates that I am not totally satisfied with the colors, but find them good enough to meet FOTD minimum standards. One thing that cannot be questioned however is the calculation time of 31 seconds. Such lightning speed can hardly be exceeded.

Web surfers may view the finished image on the FOTD web site at:

http://home.att.net/~Paul.N.Lee/FotD/FotD.html

Wednesday's weather proved to be routine here at Fractal Central. The hazy sun, temperature of 81F 27C and moderate humidity was neither good nor bad. The fractal cat Nicholas was bad however. Leaping onto the kitchen counter without looking, he spilled a carton of half-and-half. To atone for his misdeed he began lapping up the spilled cream, while Cassie cleaned the cream that dripped onto the floor.

The day was otherwise uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and where are all these indispensable wireless electronic devices coming from?

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

START PARAMETER FILE======================================= Water_Lilies { ; time=0:00:31.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 float=y inside=0 center-mag=-1.72942/0/12.8 logmap=50 symmetry=xaxis params=90/0/84/0/-0.893279/0/0/0/1.5/1.5 maxiter=1500 periodicity=10 colors=000kU9iS6gP7cM7_I8WA8S59O19N8INFQMLZMSfMYnW\ d`ekNor9jq8eq8`q7zv7zp7vp6ro6mo5ho5eo5bm7_k8Xi9SgA\ NeBKcCNaDP`ESZGVXH_VIcTJeRKhPLjNMlMNmLNnLNnLNoLNpL\ NpLNpLNpLNoLNnLNnLNoLNnNImPEmRAlPBkNCjLDjJEiIFhGGh\ EzgCzfAzf9zgBMhCPiDRjEUkFWlGzmHzmFznCzmDzpGzmJz9Mz\ ANzCPzEQzGSzITzKVzMWzOYzQZzS`zUazWczYdz_fzahz`UzZU\ zYUzWUzUUzTUzRUzQUzOUzMUzLUzJUzHUzHUzGUzGUzFUzEUzE\ UzDUzCUzCUzBUzAUzAUz9Uz8UvPOreDmv2ir7fnCcjH_fMXbRU\ ZUQVUNRUKNUGJUDFU9JUgKUgMUhOXiPRjRLkTFlRFSPG6RH8TJ\ BVLEXNHZOK`QNbSPdUSfVVhXYdTX_OWVJVQEUL9SM9UN9WP9YQ\ 8_S8aT8cV7ebFgjOjrXmK3JP3QV3X`3de3kk3rq4zp4zn5zm5y\ k6yj7xh7xg8we9wd9wbAvaAv_BuZCuXCtWDtUEsSIoQMkNQfLV\ bJZYGbUEfPCkL9oG7sC4x7BrDIlKPfQW`XbVciPipJpwCwuCws\ CwpDwnDvkEviEvfEudFuaFu_GuXGtVHtTHtQHsOIsLIsJJsGJr\ EJrBKr9Kq6Lq4Lq1Mp4Mp8LpCKqGJqKJrOIrSHsVGsZFsbFtfE\ tjDunCurBvrCsrDprEmrGjjXC } frm:DivideJulibrot { ; Jim Muth (third version) ; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z| < 1000000 } END PARAMETER FILE=========================================