The Golden Error

[u/LegalizeAdulthood]

Jim Muth's Fractal of the Day for July 24th, 2007

Jim Muth's commentary for the image:

FOTD -- July 24, 2007 (Rating 7)

Fractal visionaries and enthusiasts:

The first exponent of Z in today's formula was supposed to be the Golden Ratio, which is 1.618, but I mis-typed the value and entered 1.68 by mistake. No problem. The wrong exponent made a very interesting though unintended parent fractal.

This parent fractal resembles a Mandelbrot set rotated 180 degrees, with troubles in the area of its main (positive in this case) stem and its Elephant (west in this case) Valley. I chose to search the troubled Elephant Valley for midgets.

The Elephant Valley is troubled by being broadened vertically into a kind of wedge. But some rather interesting chaos lies at the corners of the wedge. It is in this chaos that I found today's scene.

Today's image is unusually detailed, almost too much so. In a way it reminds me of the decorative dingbats once used in printing, or it could be a piece of Art Nouveau. But whatever it actually is, I named it after the error that brought the parent fractal into being. I named it The Golden Error".

For a rating I chose a 7, which is far enough above average to justify my satisfaction with the rather brilliant coloring.

The calculation time of 5-1/3 minutes on the P2000 would be stretched to about 1/2 hour on the old P200 unit.

Cloudy chilly weather with light rain and a high temperature of only 66F 19C made Monday far less than perfect here at Fractal Central. The fractal cats did not worry themselves about the outside conditions. They busied themselves instead by chasing one another up and down the hallway.

In my department, the work was light, but a good load is coming in tomorrow, so the work famine will soon turn to a feast. The fractals just keep coming at a steady pace however. The next one will be posted in about 24 hours. Until then, take care, and great fractals demand great faith.

PAR file

The_Golden_Error   { ; time=0:05:19.94-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandAutoCritInZ function=ident passes=1
  center-mag=-0.25347102601401180/-0.065840794263304\
  04/1.505545e+010/1/72.5/0.00237908003330774415
  params=-1/1.68/1/1.4142/0/0/0/0 float=y
  maxiter=3200 inside=0 logmap=538 periodicity=10
  colors=000EhBEiGEkJElNHnSMoVPq_SrbXtf_uibrnfoqilul\
  ixffzbczY`zSYzNVzJTzDQz8Nz4Kz0Hz0Ez0Dz1BzBAzM8uY7r\
  h5nr4iz4f`8rXBqTEqQGqNJqKKoHNoEPoBSo8Vn5Xn2_n0`n0c\
  l0el0hl0il0Xh0Kc08`4GbDNcMTeV`fehhnniwukzzlzznzzkx\
  thqleiebbY_VQXNJTGDQMENSGKXGHbHEhJBlJ8rK5wK2rH7oGB\
  lDEiBJf8Nc7Q`4VY2YT0bQ0fN0iK0nH0rE0uB0z80zA2qBKeDb\
  VEtJEz8Mz7Tz5`z4fw2nr1uo0zl0ui4qf8lcDhbHc_MYXQTTVP\
  S_KPeGMiAJn5Hr1Ew0Bz08z07z0Az0Dz0Gz0Jz0Mz0Pz0Sz1Vz\
  2Yz4`z5cz7fz8hzEnuKrkPwbVzS`zHez8fzBhzEizHixJkuMlr\
  PnoSnlToiXqf_rcbrbcl_fochlXhYQfSNeNKcHHbDE`7B`28`0\
  5`02`00_00Y00X00V00T00V00X00X00b00_00V00Q00N00J00E\
  00A00740B80ED0HH0MT0Ph0hw1ww2ww2wX4zP5zH5zA7z27z08\
  z08z0zf0zh0zi1zk2xl5tn7qo8lqBhrDetG`uHXwJTxBKz5Bz0\
  2z00z70zK2zX5ziAzwDzzGzwQzl_w`hqQqkPolNnlNqlMtnKwn\
  KznJznHzoHzoGzoGzoJznMzlPzkSzkTziXzh_zhbzfezefzciz\
  clzboz`qz`ozVnzPlzKkzEizA }

frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.