|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: I almost gave up on the next formula in line, the julia(fn||fn) formula, a formula that uses the value of mod(Zn) to determine which function to apply to Zn+1. I spent nearly an hour trying different functions and different shift values, mostly getting nowhere. I found that when both functions are set to 'sqr', the well-known Z^2+C Julia sets result. It became immediately apparent that there could be no interesting function shifts when the two functions are identical. I kept trying different functions until I stumbled upon the 'recip-cos' combination while the shift value was set to 1 and the C parameter was set to 0.28, a point in East Valley of the Mandelbrot set. The resulting image was not great, but at least it was a fractal, so I searched it until I found a scene that barely makes the status of FOTD. That scene is today's image. I named the image "The Big X". When I chose the name, I might have been thinking of the movie 'It's a Mad, Mad, Mad, Mad World', where everyone was running around, looking for money buried under a mysterious 'big W'. The name is not totally unjustified. Some of the feathery elements actually do form a kind of big X on the right side of the image. I could rate the result at only a humble 4. The lowly rating is not the fault of the formula, which certainly has much more potential than I was able to find in it during the 3/4-hour or so that I worked with it. It is a complex formula that takes time to become familiar with. In fact, I am so certain that I have done the formula an injustice that I will use it again as the source of tomorrow's FOTD. Perhaps the best feature of the image is its very brief render time of 1-1/2 minutes, which combines with the rating of 4 to give an overall worth of 266 -- not such a bad value. And the minor task of rendering the image can be dispensed with entirely by downloading the finished GIF image from the FOTD web site at: Off and on rain kept things wet and the fractal cats sullen here at Fractal Central on Sunday. The high temperature of 50F 10C helped not a bit. A generous treat of tuna and turkey was needed to make Thomas stop staring me in the eye blaming me for his bad day. Tippy merely hunkered down for a good sulk until the tuna and turkey appeared. This morning is starting cloudy and chilly, but dry. I have hopes for a better day among the cats. The fractals keep coming, and the next one, the second to be created by today's julia(fn||fn) formula, will appear at this same spot in 24 hours. It almost certainly will be a better one. Until that wonderful moment arrives, take care, and fractals not only spring eternal, they winter, summer and fall eternal as well. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Big_X { ; time=0:01:30.36--SF5 on a P200
reset=2003 type=julia(fn||fn) function=recip/cos
passes=1 center-mag=-0.19876011638408430/+1.733781\
852621153/38720.9/1/-60/3.05664410449324464e-010
params=0.28/0/1 float=y maxiter=1200 bailout=6400
inside=0 logmap=36 symmetry=none periodicity=10
colors=000YGK_IKaKKcMKeOKgQKiRKlSKoTKrUKuVKxWKzXKz\
dKzlKzrKzqKzoKzmKzkKziKzgKyeKxcUwacv`muZwtXzsVzrTz\
qRzpPzoNznLzmKzkNziQzgSzfVzdXzb_z`az_dzYfzWizVkzae\
zh_zoUzvOzzJzwLzrMzmOziPzdQz_SzVTzRUzMWzHXzDYzGZzJ\
ZzMZzP_zS_zV_zX`z_`zb`zeazhazkazmbzpbzsbzvczyczzcz\
zczzazz`zyZzwYzvWztVzrTzqSzoQznPzlNzjMziKzgJzfIzdI\
zbIz`IzZIzaLzcNzfPzhRzgSzgTzgUzgVzgWzgXzfYzfZzfZzf\
_zf`zfazebzeczedzeezefzefzfezgezhdzidzjczkczlbzmbz\
nbzoazpazq`zr`zs_zt_zuZzvZzwZzsWzoTzkQzgNzcKzePzgU\
ziZzkdzmdzndzpdzrdztdzvdzwdztdzqdzodzldzidzgdzddzb\
dz_dzXdzVdzSdzPdzNdzKdzIdzKdzMdzOdzQezSezUdzVdzXcz\
Zcz`bzbbzdazeazg`zi`zk_zm_zoZzpZzqYzqYzrXzrXzsXzsW\
ztWztWzuVzuVzvUzvUzwUzwTzxTzxTzySzySzySzxUzwWzvYzu\
_ztazsczrdzqdzpdzodzndzndzmdzldzkdzjdzidzhdzgdzfdz\
edzddzddzbdzadz_dzZdzYdzWdzVqzUnzSlzRizQfzOczN`zLZ\
zKWzJTzHQzGOzFLzDIzCFzBDz }
END PARAMETER FILE=========================================
|
times.
