Fractal visionaries and enthusiasts: 

The math behind today's image combines 4 parts of Z^2 with 3 parts of Z^4 and 2 parts of Z^3, then subtracts a whopping 100 parts of Z^5 before adding C on each iteration.  This crazy mixture creates a parent fractal shaped somewhat like a sickle cell, with X-axis symmetry and a large main spike pointing west.

This large period-2 bud on the negative X-axis appears quite normal, but the shapes of the other buds around the main bay are wildly varied.  Today's scene is located in a bud on the northeast shore of the large sickle-shaped main bay of the parent.

I did not try to find an additional critical point of the generating expression.  The value of zero so frequently works as a critical point with this formula that I generally try it first.  In today's case, zero works quite well, though I might check for other critical points and see what kind of parent fractal results.

The unusual coloring effect in today's image was achieved by rendering the scene with the outside set to 'fmod' with the proximity unchanged from the default 0.01.  This is what inspired the name "Proximity 0.01".

With a rating of 7-1/2, the artistic value, at least in my opinion, is worth a little more than the math value, which rates a whole-number 7.

The MandelbrotMix3a formula is a slow one, which slows the calculation to a turtle-like 3 minutes.  So don't let the turtle win the race.  Check the finished image at one of the web sites.

Today here at Fractal Central began with cloudy skies, but the clouds cleared off by noon, leading to a pleasant, mostly sunny afternoon with a temperature of 75F 24C, low humidity and a refreshing north wind.  The fractal cat, fully refreshed, spent the afternoon watching the local pigeons, which are starting to get out of control and might eventually have to be cleared from the surrounding eaves.  The fractal humans had a routine day, as most days are here at FC.

The next FOTD will be posted in the right time.  Until that time arrives, take care, and some conservatives wonder why so many people have chosen to live homosexual lives and suffer the resulting social rejection and possible hellfire.  Too bad!  These puzzled conservatives will never find the answer.

Jim (neither right nor left) Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

Proximity_0.01     { ; time=0:03:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix3a function=ident passes=1
  center-mag=+0.05921017762628365/+0.181266449610439\
  /4.5583e+008/1/82.5/0 params=4/2/3/4/2/3/-100/5/0/0
  float=y maxiter=600 inside=0
  outside=fmod periodicity=6
  colors=000UU5UV4UU4UT4UQ5UN6UK6UH7UF7UC8U99U69U3AU\
  1AUeoVZgVS`WLTWEMX7EX07Z3C`5Hb7Md9RfBWhE`jGelIjnKo\
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  4OB4NC4MC4MD4LD4LE4KE4JF4JF4IG4IH4HH4GI4GI4FJ4EJ4E\
  K4DK4DL4CL4BM4BM4AN4AN49O48O48P47P47O59O6AN7BN8CM9\
  DMAFLBGLCHKDIKEJJFKJGMIHNIIOHJPHJQGKRGLTFMUFNVEOWE\
  PXDQYDR_CS`CTaBUbBVcAWdAXf9Yg9Yh8Zi8_j7`k7am6bn6co\
  5dp5eq4fr4gt3hu3iv2jw2kx2ky4jv5jt6jq8jo9ilAijCigDi\
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  jCUkGTmJSnNSpQRqURsXQt`PvcPwgOyjOzmPvjQshRpeRmcSj`\
  TgZTdWUaUVZRVWPWVMcNKcIHcFFcGCcDAcA7d75e42f10e22a3\
  3Z34V46S57O58L6AH7BF7CC6EA6F76G56I27J08K18M28O39P4\
  AR5BS6CU7DV8EX9FZAG_BHaCIbDJdEKeFLgGMiHNjIOkJPlKQm\
  LQnMRoMRoMSoNSoNSoNTnOToOTnOUnPUnPUnPUnQUnQUnQUnRU\
  nRUnRUnSVnSWnSWmSWmSWm6CU }

frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }

END PARAMETER FILE=========================================