Fractal visionaries:

I've done it again -- I've made another boo-boo in my F.O.T.D.  In yesterday's post I said that the fractal image "Spires" lay in the true Mandelbrot plane of the Z^3+(0.2*Z^3) fractal.  The image most certainly does not.  While looking over the fractal's parameters earlier today, I noticed that p3 was set to 0+.3i, not the 1,0 which would have put the image in the true plane  It's only a small error, but I try to be as accurate as my limited knowledge will permit.

Today's fractal, "Tiles", is a brief departure from my usual stuff.  The name needs no explanation.  It looks almost exactly like what one would see on the wall around the bath.

The formula has been lying unused in my hold file for a while.  It is my own reworking of a formula I picked up somewhere on the net several months ago.  It might even have been from someone in the Fractal-Art group -- I don't recall.  But whatever its source, it's pretty effective at producing tile-like fractals.  Simply set p1 to the coordinates of an interesting area of the Mandelbrot set, and watch the fun as you try the thousands of function combinations.

The image has been posted to a.b.p.f. and a.f.p. for those who have access to those groups. 

Now I must explain how I colored yesterday's image.  Yesterday's fractal took advantage of a feature of Fractint that is not too often used -- the ranges feature.  As I explained in the article, in all slices of the julibrot figure except the Julia slices and the true Mandelbrot slice, the low and high iteration areas of the image behave like independent entities, often doing apparently unrelated things.

When I use the ranges feature, I take advantage of this peculiarity by coloring the high and low iteration parts with contrasting colors, which emphasizes the different dynamics, and using banding on the low-iteration areas, which gives these low parts a rather convincing three-dimensional appearance.

The most effective point to change from low-iteration bands to the high iteration colors must be found by experiment, but it is usually about one-tenth of the fractal's maxiter.  The higher the magnitude of the fractal, the higher the change point must be.

Tomorrow, I'll most likely return to my favorite fractal -- the julibrot.

Until then, may all your fractals be great ones.

Jim Muth
jamth@mindspring.com


START 19.6 FILE=============================================

Tiles              { ; time=0:00:04.95-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=Mosaic function=conj/cotan/flip/cotan
  passes=1 center-mag=0/0/0.07978936/0.8896
  params=0/0.68 float=y maxiter=90 inside=bof60
  logmap=yes symmetry=xyaxis periodicity=10
  colors=000OjVHApF8pD7pA5p83pU8ZZE`cLbiRcnYescgtjpu\
  qxuapu_nuYltWitUgtSetQctOasNZsLXsJVsHTsFRrDOrBMr9K\
  nDMjHNgLPcPQ_USWYTTaVPeWLiYPgWTdTWbR_`PcYNgWKkTIoR\
  GrPEvMBzK9vOBqSDmVGiZIdbK`fMXiPSmROqTTzcPxWLwP8toD\
  uZMHBKVEJhGklQRP`PYWMeRKnMzlce5oYNcQdTTOUQXRNeOKnL\
  _7aXf_SlUNqOv0jMq9KtEIexgzs`yiVx`OwR0AU9ZOE1Aun9ar\
  E`f3RnBb5FSWHw`ubkaXxoIdaImSF9mHYYIKKIXJIiItY`gfUV\
  nOmC3eO7Y_BQkFtrMu`gakVMKvoKkXKkTIiPFfMDdIAaE8_A5X\
  XI_rUblTdfTg`SiVSlPRnZSeiTWsUNrVPpWRoXTmYVlZXj_Zi_\
  ag`cfaedbgcciadk`emdWogNrkDtn3vn5un7snArmCpmEomGmm\
  JlmLjmNimPglRflUdlWclYai`ZfbXbeU_gRXjPUlMRoJNqGKtE\
  HvBIvFZFBqDYhPU__QRkMWCZP_Qx6B2`bAkSxjwH91HM5IYAIj\
  E78MDYKg3NXVNPGtLa`ZlpVogQqZMtQt9igQ_VfR0Ig6WZCiQY\
  FkSUaNhSqVZhaV_hQRoMZyHVxHQwIMvI`p8WrBRsDMuGldxdim\
  XmbPrSFqAsYnePgkVgp`gvfg_QZE9RaLQxWQr_RkdSehTZlTTq\
  UMuV5fcAlWEqP_TVWv7RvBMvF }

frm:Mosaic {; thanks to someone unknown
; p1=Mandelbrot set coordinates
z=c=p1+.05*(fn1(fn2(real(pixel)))+flip(fn3\
(fn4(imag(pixel))))):
z=sqr(z)+c,
|z| <= 100 }

END 19.6 FIL3======================================================