Fractal visionaries:

Today's formula is a really strange one.  One minute it's drawing the classic Mandelbrot set, the next minute it's drawing a screen full of flying fragments.  I devised the formula in an effort to eliminate the break along the negative x-axis that appears when complex or imaginary powers are calculated.  I got a lot more than I bargained for.

I figured that since positive and negative imaginary powers draw fractals that spiral around the origin in opposite directions, if an expression something like (Z^2i)^(Z^(-2i)) were calculated, the opposite signs would cancel the spiraling out, leaving a fractal with the features of an imaginary exponent without the discontinuity along the x-axis.

It worked beautifully.  Today's fractal, ringwrld, shows a somewhat distorted but still recognizable Mandelbrot set surrounded by rings introduced by the imag(1) assigned p3, which is calculated in the formula as both positive and negative.

The formula is full of other surprises.  It's one of the most bizarre and unpredictable formulas in my collection, but despite its versatility, it still runs fast.  So don't hesitate to change the parameters and see what surprises you can turn up.

Jim Muth
jamth@mindspring.com


START PARAMETER-FORMULA FILE FOR 19.6==============================

Brot_in_a_Spot     { ; time=0:00:04.94-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Mytest06 center-mag=-0.729122/0/0.4411
  params=1/0/0.5/0/0/1 float=y bailout=100 inside=253
  logmap=yes symmetry=xaxis periodicity=10
  colors=000OMJUOG_PDeRBkS8qU5wV2wY4w_6wb8xe9xhBxjDx\
  mFugDraBoW9mR8jL6gF4d92a301`udQTbdgarudsngthjualwV\
  oxOryIuzBqvFmqJimNdhS`dWX__TWcYdUbmKbhOccTcZXdUadP\
  eSPWGON3OD3ND3MD3KC3JCbPePSOCU6KXOR`fZcx`iobofdtXf\
  zO9BsECtKEuPFvUGw0s46s6Cr8HrANrDTqFZqHcpJipL_UTR8_\
  ZIafSdmafukhdnPPq6UgAZYEbOHgELl4Pg7UcAZZDcVHhQKmMN\
  rHQwLQoOQgSQ_WPR_PJbPBfP3aU6XY9SbCNfFIkHDoK8tN3xQF\
  tSRqUbmWniYKHsr5wm6vh8vc9uZAuUBtPDtKEsanLZiPWeUT`Y\
  RXbOSfLOkIJoI4SH7ZHAeGDlr68h8KZBWPDg1Ns5Ls9JsDHsEK\
  BFIQGGdeVfbThZRjWPkSNmPLoWO6_L8dIAhEClBEgRBIdFKbIN\
  aKP_NHKF95898A8CB8FD7IE7MG7PH6SJ6WK5ZM5aN4eP4hQ8gR\
  CfRGfSKeTOdTScUWcV_bWcaWg`Xk`Yo_YsZZrZXp_Uo_Sm_Pl`\
  Nj`Ki`IgaFfaDdaAcb8ab5`b3Za6Xa9V`CT`FR_IP_LN_OMZRK\
  ZUIZXGY_EYbCXeAXhf9Wl9_jA_iB_iIVhPQhWKgbFN5xHAjCFX\
  6KI0P4coIYkJSgKYjIclHbnKaoO`qR_rUZtXYu`XwcWxfZx`ax\
  VdxPfwKiwElw8ow200LMWCOSF }

frm:Mytest06  {; Jim Muth
z=c=pixel:
z=(((z^p1)*(z+p2))^p3)^(-p3)+c,
|z|<100 }

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