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May 12, 1997: Seven Magnificent Minibrots May 11 May 13 1997 FOTD Home

seven

Fractal visionaries:

Over the past 7 years, I have probably written and deleted thousands of formulas.  Most of these were discarded because they produced either a blank screen or duplicated figures that were more easily drawn with simpler formulas.  Only a few survived to find a permanent home in my formula file.  Today's formula, Test15, is one of the survivors.  I've yet to get around to naming it.

I thought of the formula today because I've been reading lately of formulas that draw multiple midgets in a circle.  One thing today's formula does, among many others, is to draw any number of midgets of any order, facing either in or out, in a circle around the origin.  Today's picture, seven_up, shows seven midgets of order two, arranged in a circle facing outward.  To have them face inward, change the +0.35 assigned real p2 to -0.35.

I'll leave it to the intrepid fractal explorers to discover how to change the number of midgets, or how to change their shape to midgets of a different order.  I'll give only the caution that it's easy to get hopelessly lost.  But even if you get lost, you'll see some strange sights.

It's a tricky process involving several parameters that must be changed and coordinated at the same time.  (OK, if anyone really wants to know, I'll send the method along, but be warned that the description of the method is mathematically convoluted and will make rather tedious reading.)

To atone for today's fractal, which is much math and little art, I'll post a great piece of fractal art tomorrow.

Jim Muth
jamth@mindspring.com


START COMBINED FILE FOR 19.6====================================

Seven_Magnificent  { ; time=0:00:02.91-SF5 on P4-2000
  reset=2004 type=formula formulafile=jim.frm
  formulaname=Test15 center-mag=-0.00126273/0/0.51461
  params=0.25/4/0.35/-3/2/1 float=y maxiter=90
  inside=0 outside=tdis symmetry=xaxis periodicity=10
  colors=000000eJ`_ESU9JO4AMIBLVCJgDItEzeLzURzzXzzSz\
  zOzzsrTsQu8Qu8Qt8Qt9Qs9Qs9Qs9QrAQrAQqAQqAQqBQpBRpB\
  RoBRoCRnCRnCRnCRmDRmDRlDRlDRlERkERkERjERjFRjFRiFRi\
  FShGShGSgGSgGSgHSfHSfHSeHSeISeISdISdIScJScJScJSbJS\
  bKSaKTaKT`KT`LT`LT_LT_LTZMTZMTZMTYMTYNTXNTXNTXNTWO\
  TWOTVOTVOgJK_PMTVOL`QGdGFeKEeNEeRDeUCfYCf`BfcAfgAg\
  j9gn8gq7hw8gt8gr9gp9gnAflAfjAfgBfeBecCeaCe_CeYDdVD\
  dTEdREdPFcNFcLFcIGcGGbEHbCHbAFd5Gc7Hb8IaAJaBK`CL_E\
  MZFNZHOYIPXJQWLRWMSVNSUPTTQUTSVSTWRUXQWYQXZPY_O_`O\
  `aNbbMccLddLfdKgeJifIjgIkhHmiGnjFokFqlErmDtnCuoCvp\
  BxqAyqAzoDwmFukHriJpgLmeNkcQhaSf_UcYWaWYZU_XSbUQdS\
  OfPMhNKjKGmGHlHIlIJlIJkJKkKLkKMjLMjLNjMOjNPiNPiOQi\
  PRhPShQShQThRUgSVgSVgTWfUXfUYfVXiWYhVYgVYfVZfUZeUZ\
  dUZdU_cT_bT_aT_aT``S`_S`_S`ZRaYRaXRaXRaWQbVQbVQbUQ\
  bTPcSPcSPcROcQOdQOdPOdONdNNeNNeMNeLMeLMfKMfJLfILfI\
  LgHLgGKgGKgFKhEKhDJhDJhCJ }

frm:Test15 {; Jim Muth
z=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3), g=f*(pixel):
z=((a*(z^b))+(c*(z^d)))^k+g,
|z| <= 100 }

END COMBINED FILE FOR 19.6======================================
END VERSION 19.6 FORMULA-PARAMETER FILE=========================