; July 24, 1997: Tiles 
;
; tiles
;
; 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======================================================
;