; July 16, 1997: On a Crooked Spike 
;
; spike
;
; 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
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}

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===============================================
;