Fractal visionaries:

Today's fractal was supposed to be more art and less theory.  Well, I had good intentions, but I got too involved with that test formula that I posted yesterday.  While noodling around with it this evening, I realized that real p3, which moves the displayed slice along the X-axis, actually determines the axis of rotation.  To see how this works, simply set real p3 to -0.75 (Seahorse Valley) and watch the entire figure rotate on the -0.75 axis-line.  Real p2 moves the displayed slice along the Z-axis, and imag p2 moves it along the W-axis.  Imag p3 moves the image along the Y-axis, but this does nothing more than shift the position of the images on the screen

This arrangement is still not perfect, since the parallel oblique slices do not move perpendicularly to the plane being displayed, which causes the image to shift position on the screen.  This can be corrected by applying a corresponding rotation, but at this time I'm mentally congested, and since all slices can be displayed as the formula now stands, I think I'll let the formula rest.

I have re-attached yesterday's formula below, because as Jay Hill pointed out, my degree conversion factor was a bit off the mark.  The inaccuracy was very slight, but it did make a difference at the highest magnifications.  When I wrote the formula, I recalled only six digits.  Being lazy, I filled in the rest with 3's instead of looking up the correct value.

Today's formula is a generalization of yesterday's formula to any real power of Z.  I made the bailout a variable because changing the bailout has a very significant effect on the appearance of the negative power mandeloids.  Today's fractal is a tiny midget on one of the infinity of negative tails of the Z^2.002 mandeloid, sliced at an angle of 75 degrees from the XY direction.  I named it "Swirls" because of the obvious swirling effect of the bits and pieces of negative tails around the midget.  One word of warning -- don't use today's formula (XY-YZ-test03) to draw slices of the Z^2 set.  It's less that half as fast as yesterday's XY-YZ-test02 formula on the Z^2 set.

The finished image has been posted to a.b.p.f. and a.f.p.  For tomorrow, most likely I'll post another odd angle image.  I picked up enough oblique ideas from Benno's Julibrot web page to keep me busy for a year.

Jim Muth
jamth@mindspring.com


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

On_a_Crooked_Spike { ; time=0:00:26.47-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm float=y
  formulaname=XY-YZ-test03 passes=1 center-mag=-0.11\
  45278127801932/+0.00909585091588167/2395.932/0.116\
  /3.229/63.701716 params=75/2.002/0/0/-1.7545/36
  maxiter=3600 inside=0 logmap=yes periodicity=10
  colors=000Oh`Ok`NiZMgYLeWKcVJaTI_RHYQGWOFUMESLDPJC\
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  kPokQnkRlkSjkTikUglVflWdlXblYalZ_l_Yl`XlaVlbTlzSlz\
  QlzOmzNmzLmzKmzImzGmzFmzDszLyzSxzRvzPuzOszNrzLqzKo\
  zJnzHlzGkzEizDhzCgzAez9dz8bz6az5XzASzENzJzmzzmzzmz\
  zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzMpgMofNneNmcOlb\
  OkaPj`Pi_QhZQgYRfXSeWSdVTcUTbTUaSU`RV_QVYOWXNWWMXV\
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  WR9WS9VUAUVBUWBTXCSYCRZDR_EQ`EPaFObFOdGNeHMfHLgILh\
  IKiJRNeRQdQTdQXcP_bPbbOea }

frm:XY-YZ-test03 {; Jim Muth
; real(p1)=rotation angle in degrees,
; imag(p1)=exponent of z
; p2=parallel planes, real(p3)=axis of
; rotation and parallel planes
; imag(p3) = escape radius
z=sin(real(p1)*.01745329251994)*real(pixel)+p2,
c=cos(real(p1)*.01745329251994)*real(pixel)+flip\
(imag(pixel))+real(p3):
z=z^imag(p1)+c,
|z| <= imag(p3) }

END 19.6 FILE===============================================