Your IP : 216.73.216.48
RCL_Pick1 (XAXIS) { ; Ron Lewen, 76376,2567
; Try corners=2.008874/-3.811126/-3.980167/3.779833/
; -3.811126/3.779833 to see Figure 9.7 (P. 123) in
; Pickover's Computers, Pattern, Chaos and Beauty.
; Figures 9.9 - 9.13 can be found by zooming.
; Use floating point
z=0:
z=cosh(z) + pixel,
abs(z) < 40
}
RCL_Pick10 (XAXIS) { ; Ron Lewen, 76376,2567
; Variation of Figure 9.18 (p.134) from Pickover's
; Book. Generates an interesting Biomorph.
z=pixel:
z=z/pixel-pixel*sqr(z),
abs(z) < 8
}
RCL_Pick11 (XAXIS) { ; Ron Lewen, 76376,2567
; Formula from Figure 8.3 (p. 98) of Pickover's
; book. Generates a biomorph. Figure 8.3 is a
; zoom on one of the shapes at the corner of the
; biomorph.
; Use Floating Point
z=pixel:
z=z^2+0.5
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_Pick12 { ; Ron Lewen, 76376,2567
; Formula from Figure 12.7 (p. 202) of Pickover's
; book.
; Use Floating Point
z=pixel:
z=(2.71828^(p1)) * z * (1-z),
abs(real(z)) < 10 || abs(imag(z)) < 10
}
RCL_Pick13 { ; Ron Lewen, 76376,2567
; Formula from Frontpiece for Appendix C
; and Credits in Pickover's book.
; Set p1=(3,0) to generate the Frontpiece
; for Appendix C and to (2,0) for Credits
; Use Floating Point
z=.001:
z=z^p1+(1/pixel)^p1,
|z| <= 100
}
RCL_Pick2_J { ; Ron Lewen, 76376,2567
; A julia set based on the formula in Figure 8.9
; (p. 105) of Pickover's book. Very similar to
; the Frontpiece for Appendix A.
z=pixel:
z=sin(z) + z^2 + p1,
abs(real(z)) < 100 || abs(imag(z)) < 100
}
RCL_Pick2_M (XAXIS) { ; Ron Lewen, 76376,2567
; Generates a biomorph of a Pseudo-Mandelbrot set with
; extra tails. Part of Pickover's Biomorph Zoo Collection
; Formula is adapted from Pickover's book, Figure 8.9
; (p. 105) but the result is different. Set corners=
; -2.640801/1.359199/-1.5/1.5 to center image. I use the
; color map that comes as default in WINFRACT. (I guess I
; like purple <G>).
; Use floating point
z=pixel:
z=sin(z) + z^2 + pixel,
|real(z)| < 100 || |imag(z)| < 100
}
RCL_Pick3 (XAXIS) { ; Ron Lewen, 76376,2567
; Generates Figure 9.18 (p. 134) from Pickover's book.
; Set maxiter >= 1000 to see good detail in the spirals
; in the three large lakes. Also set inside=0.
z=0.5:
z=z*pixel-pixel/sqr(z),
abs(z) < 8
}
RCL_Pick4 (XAXIS) { ; Ron Lewen, 76376,2567
; Variation of formula for Figure 9.18 (p. 134) from Pickover's
; book.
; Set inside=0 to see three large lakes around a blue "core".
z=pixel:
z=z*pixel-pixel/sqr(z),
|z| <= 4
}
RCL_Pick5 (XAXIS) { ; Ron Lewen, 76376,2567
; Adapted from Pickover's Biomorph Zoo Collection in
; Figure 8.7 (p. 102).
z=pixel:
z=z^z + z^5 + pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_Pick6 (XAXIS) { ; Ron Lewen, 76376,2567
; Adapted from Pickover's Biomorph Zoo Collection in
; Figure 8.7 (p. 102).
z=pixel:
z=z^z + z^6 + pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_Pick7 (XAXIS) { ; Ron Lewen, 76376,2567
; Adapted from Pickover's Biomorph Zoo Collection in
; Figure 8.7 (p. 102).
z=pixel:
z=z^5 + pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_Pick8 (XAXIS) { ; Ron Lewen, 76376,2567
; Adapted from Pickover's Biomorph Zoo Collection in
; Figure 8.7 (p. 102).
z=pixel:
z=z^3 + pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_Pick9 (XAXIS) { ; Ron Lewen, 76376,2567
; Adapted from Pickover's Biomorph Zoo Collection in
; Figure 8.7 (p. 102).
z=pixel:
z=sin(z) + 2.71828^z + pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_Quaternion_J (ORIGIN) { ; Ron Lewen, 76376,2567
; From Pseudocode 10.56 (p. 169) of Pickover's book.
; Looks at Julia set for a0,a2 plane. p1 selects
; slice in to look at.
; p2 corresponds to a point on the Quaternion
; Mandelbrot set (see below).
; Try (-.745,.113) as a starting point.
a0=real(pixel), a2=imag(pixel), a1=real(p1), a3=imag(p1):
savea0=a0^2-a1^2-a2^2-a3^2+p2,
savea2=2*a0*a2+p2, a0=savea0, a2=savea2,
(a0^2+a1^2+a2^2+a3^2) <= 2
}
RCL_Quaternion_M (XAXIS) { ; Ron Lewen, 76376,2567
; From Pseudocode 10.5 (p. 169) of Pickover's book.
; Looks at Mandelbrot set for a0,a2 plane.
; p1 selects slice in to look at. p1 should
; not be (0,0) (this yields a blank screen!).
a0=a2=pixel, a1=real(p1), a3=imag(p1):
savea0=a0^2-a1^2-a2^2-a3^2+pixel,
savea2=2*a0*a2+pixel, a0=savea0, a2=savea2,
(a0^2+a1^2+a2^2+a3^2) <= 2
}
REB004A = {; Ron Barnett [70153,1233]
; try p1 = 0.9, p2 = 2, fn1 = sin, fn2 = cos
z = pixel:
z =p1*fn1(z) + p1*p1*fn2(p2*z) + pixel, |z| <= 100
}
REB004B = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = 3
z = pixel:
z = pixel + p1*(z/2 + z*z/6 + z*z*z/12), |z| <= 100
}
REB004C = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = 3, p2 = (-0.009,1.225)
z = pixel:
z = p2 + p1*(z/2 + z*z/6 + z*z*Z/12), |z| <= 100
}
REB004D = {; Ron Barnett [70153,1233]
; try p1 = -1, fn1 = sin
z = pixel:
z = pixel + fn1(2*z+1)/(2*z+p1), |z| <= 100
}
REB004E = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = -1, p2 = -1, fn1 = sin, fn2 = cos
z = pixel:
z = pixel + fn1(2*z+1)/(2*z+p1);
z = z + fn2(4*z+1)/(4*z+p2), |z| <= 100
}
REB004F = {; Ron Barnett [70153,1233]
; try p1 = -1, p2 = (-0.92, 0.979), fn1 = sin
z = pixel:
z = p2 + fn1(2*z+1)/(2*z+p1), |z| <= 100
}
REB004G = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = -1, p2 = (0.849,0.087), fn1 = sin, fn2 = cos
z = pixel:
z = p2 + fn1(2*z+1)/(2*z+p1);
z = z + fn2(4*z+1)/(4*z+p1), |z| <= 100
}
REB004H = {; Ron Barnett [70153,1233]
; floating point required
; try fn1 = sqr
z = pixel:
z = pixel + fn1(3/z - z/4), |z| <= 100
}
REB004I = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = (-1.354, 0.625) fn1 = sqr
z = pixel:
z = p1 + fn1(3/z - z/4), |z| <= 100
}
REB004J = {; Ron Barnett [70153,1233]
; floating point required
; try fn1 = tan
z = pixel:
x = flip(pixel + fn1(3/z - z/4));
z = x*z + pixel, |z| <= 100
}
REB004K = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = (-0.564, 0.045), fn1 = tan
z = pixel:
x = flip(pixel + fn1(3/z - z/4));
z = x*z + p1, |z| <= 100
}
REB004L = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = 1, p2 - 2, fn1 = tan
z = pixel:
x = flip(pixel + fn1(p1/z - z/(p2+1)));
z = x*z + pixel, |z| <= 100
}
REB004M = {; Ron Barnett [70153,1233]
; floating point required
;try p1 = (0.4605, 0.8), fn1 = tan, fn2 = cos
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1(const - 12*x)*x/(4*const);
y1 = -fn2(const + 12*x)*y/(4*const);
x2 = x1*x1 - y1*y1 + p1;
y2 = 2*x*y;
z = x2 + flip(y2), |z| <= 100
}
REB004N = {; Ron Barnett [70153,1233]
z = 0.5:
x = pixel*(z - 1/z) + p1,
z = pixel*(x - 1/sqr(x) + p2), |z| <= 100
}
REB005A = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = 0.77, fn1 = ident, fn2 = ident
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1(const - 12*x)*x/(4*const);
y1 = -fn2(const + 12*y)*y/(4*const);
x2 = x1*x1 - y1*y1 + p1;
y2 = 2*x1*y1;
z = x2 + flip(y2), |z| <= 100
}
REB005B = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = 0.01, fn1 = ident, fn2 = ident
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1(const - x)*x/const;
y1 = -fn2(const + y)*y/const;
x2 = x1*x1 - y1*y1 + p1;
y2 = 2*x1*y1;
z = x2 + flip(y2), |z| <= 100
}
REB005C = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = -0.5, p2 = -0.1, fn1 = ident, fn2 = ident
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1(const + p1*x)*x/const;
y1 = -fn2(const + y)*y/const;
x2 = x1*x1 - y1*y1 + p2;
y2 = 2*x1*y1;
z = x2 + flip(y2), |z| <= 100
}
REB005D = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = -1, p2 = -1, fn1 = sin, fn2 = ident
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1((const + p1*x)*x/const);
y1 = -fn2((const + y)*y/const);
x2 = x1*x1 - y1*y1 + p2;
y2 = 2*x1*y1;
z = x2 + flip(y2), |z| <= 100
}
REB005E = {; Ron Barnett [70153,1233]
; floating point required
; try p1 = (0,0.09), fn1 = sin, fn2 = tan
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1((const - x)*x/const);
y1 = -fn2((const + y)*y/const);
x2 = x1*x1 - y1*y1 + p1;
y2 = 2*x1*y1;
z = x2 + flip(y2), |z| <= 100
}
REB005G = {; Ron Barnett [70153,1233]
; floating point required
; try fn1 = ident, fn2 = sin
z = pixel:
x = real(z), y = imag(z);
const = x*x + y*y;
x1 = -fn1(const + p1*x)*y/const;
y1 = -fn2(const + y)*x/const;
x2 = x1*x1 - y1*y1 + p2;
y2 = 2*x1*y1;
z = x2 + flip(y2), |z| <= 100
}
REBRefInd1 = {; Ron Barnett [70153,1233]
; Use floating point
; p1 = 1, p2 = 2, fn1 = sin, fn2 = sqr
z = pixel:
z = (z*z-p1)/(z*z+p2)*fn1(z)*fn2(z) + pixel,
|z| <= 100
}
REBRefInd2 = {; Ron Barnett [70153,1233]
; Use floating point
; try p1 = (0.489, 0.844), fn1 = sin, fn2 = sqr
z = pixel:
z = (z*z-1)/(z*z+2)*fn1(z)*fn2(z) + p1,
|z| <= 100
}
REBRefInd3 = {; Ron Barnett [70153,1233]
; Use floating point
; p1 = (0.48, 0.67), fn1 = sin
z = pixel:
z = (z*z-1)/(z*z+2)*fn1(z) + p1,
|z| <= 100
}
REBRefInd4 = {; Ron Barnett [70153,1233]
; Use floating point
; try p1 = 1, p2 = 2, fn1 = cosh, fn2 = sqr
z = pixel:
z = flip(z);
z = (z*z-p1)/(z*z+p2)*fn1(z)*fn2(z) + pixel,
|z| <= 100
}
REBRefInd5 = {; Ron Barnett [70153,1233]
; Use floating point
; try p1 = (0.46, 0.482), fn1 = cosh, fn2 = sqr
z = pixel:
z = flip(z);
z = (z*z-1)/(z*z+2)*fn1(z)*fn2(z) + p1,
|z| <= 100
}
RecipIke = {; Ron Barnett [70153,1233]
; try p1 = (-1.44,-0.4) with royal.map
z = pixel:
z = 1/(z*z*z + (p1-1)*z - p1),
|z| <= 4
}
quadrants {
; floating point is recommended
z=0, c=pixel,
r1=(0.0,1.0), r2=(-1.0,0.0), r3=(0.0,-1.0), r4=1:
z=sqr(z)+c,
x=real(z), y=imag(z),
xp=(0 < x), xn=(x < 0), yp=(0 < y), yn=(y < 0),
k1=xp*yp, k2=xn*yp, k3=xn*yn, k4=xp*yn,
k=k1*r1+k2*r2+k3*r3+k4*r4,
c=c+k*p1/z,
|z| <= 4
}
Sam_0(XAXIS) = {; from SAM.FRM
z = Pixel:
z = z^z - pixel
}
Sam_1(XAXIS) = {; from SAM.FRM
z = Pixel:
z = z^(-z) - pixel
}
Sam_10(XYAXIS) = {; from SAM.FRM
z = Pixel:
z = sin(1/z)
}
Sam_11(XAXIS) = {; from SAM.FRM
;Try this with periodicity=none command line
z = Pixel:
z = sinh(1/z)
}
Sam_2(XAXIS) = {; from SAM.FRM
; use integer math, not floating point or you will get a blank screen
z = Pixel:
z = z^(1/z) - pixel
}
Sam_3(XAXIS) = {; from SAM.FRM
z = Pixel:
z = z^z^z - pixel
}
Sam_4(XAXIS) = {; from SAM.FRM
z = Pixel:
z = z^(z^(1/z)) - pixel
}
Sam_5(XAXIS) = {; from SAM.FRM
z = Pixel:
z = z^2.718281828 + pixel
}
Sam_6(XYAXIS) = {; from SAM.FRM
z = Pixel:
z = z*cos(z) - pixel
}
Sam_7(XAXIS) = {; from SAM.FRM
z = Pixel:
z = z*sin(z) - pixel
}
Sam_8 = {; from SAM.FRM
;fix by Ron Barnett [70153,1233]
z = c = Pixel:
z = z^c
}
Sam_9(XYAXIS) = {; from SAM.FRM
z = Pixel:
z = z*tanh(z)
}
ScottLPC(XAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = log(z)+cosxx(z),
|z|<TEST
}
ScottLPS(XAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = log(z)+sin(z),
|z|<TEST
}
ScottLTC(XAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = log(z)*cosxx(z),
|z|<TEST
}
ScottLTS(XAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = log(z)*sin(z),
|z|<TEST
}
ScottSIC(XYAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = sqr(1/cosxx(z)),
|z|<TEST
}
ScSkCosH(XYAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = cosh(z) - sqr(z),
|z|<TEST
}
ScSkLMS(XAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = log(z) - sin(z),
|z|<TEST
}
ScSkZCZZ(XYAXIS) {; Lee Skinner [75450,3631]
z = pixel, TEST = (p1+3):
z = (z*cosxx(z)) - z,
|z|<TEST
}
Silverado(XAXIS) {; Rollo Silver [71174,1453]
; Use floating point.
; Select p1 such that 0. <= p1 <= 1.
z = Pixel, zz=z*z, zzz=zz*z, z = (1.-p1)*zz + (p1*zzz),
test = (p2+4)*(p2+4):
z = z + Pixel, zsq = z*z,
zcu = zsq*z, z = (1.-p1)*zsq + p1*zcu,
|z| <= test
}
Silverado2 { ; Rollo Silver [71174,1453]
; Use floating point.
st=1-p1,zz=pixel*pixel,z=zz*pixel*real(p1)+zz*real(st):
z=z+pixel,
zz=sqr(z), ; and save mod in lastsqr
z=zz*z*real(p1)+zz*real(st),
4 > lastsqr
}
SinEgg(XAXIS_NOPARM)[float=y function=sin/sqr] {; Jonathan Osuch
; Generalized by Tobey J. E. Reed [76437,375]
; Try p1=0, p2=4, fn1=sin, fn2=sqr
; Try p1=0, p2=4, fn1=sinh, fn2=sqr
; Use floating point.
z = p1, x = |z|:
IF (1 < x)
z=fn1(z) + pixel
ENDIF
z = fn2(z)+pixel
x = |z|
x <= p2
}
SinInvZ(XYAXIS) = {
z=pixel, inv=1/pixel+p1:
z=sin(inv/z),
|z|<=4
}
SinhInvZ(XYAXIS) = {
z=pixel, inv=1/pixel+p1:
z=sinh(inv/z),
|z|<=4
}
Something (xaxis) = {
z = pixel:
z = pixel + z*z + 1/z/z,
|z| <= 4
}
Somethingelse (xyaxis) = {
z = 1:
z = pixel * (z*z + 1/z/z),
|z| <= 1000000
}
SymmIcon {; Darell Shaffer [76040,2017]
z = P1, x = P2,
bar = (1,-1),
l = real(P1), a = imag(P2),
b = .2, g = .1, w = 0, n = 5:
zbar = z*bar;
z = ((l +(a *z *zbar) +(b *real(z^n)) +(w *i)) *z) +g *(zbar^(n-1)) +pixel;
}
SymmIconFix {; Darell Shaffer [76040,2017]
; Fix by Jonathan Osuch
z = P1, x = P2,
l = real(P1), a = imag(P2),
b = .2, g = .1, w = 0, n = 5:
zbar = conj(z);
z = ((l +(a *z *zbar) +(b *real(z^n)) +(w *i)) *z) +g *(zbar^(n-1)) +pixel;
}
TanInvZ(XYAXIS) = {
z=pixel, inv=1/pixel+p1:
t=inv/z,
z=sin(t)/cos(t),
|z|<=4
}
TanhInvZ(XYAXIS) = {
z=pixel, inv=1/pixel+p1:
z=tanh(inv/z),
|z|<=4
}
test {; Michael Theroux [71673,2767]
;fix and generalization by Ron Barnett [70153,1233]
;=phi
; try p1 = 2.236067977 for the golden mean
z = ((p1 + 1)/2)/pixel:
z = z*z + pixel*((p1 + 1)/2),
|z| <= 4;
}
test1 {; Michael Theroux [71673,2767]
;fix and generalization by Ron Barnett [70153,1233]
;=phi
; try p1 = 2.236067977 for the golden mean
c = pixel,
z = ((p1 + 1)/2):
z = z*z + pixel*((p1 + 1)/2) + c,
|z| <= 4;
}
test2 {; Michael Theroux [71673,2767]
;fix and generalization by Ron Barnett [70153,1233]
;=phi
; try p1 = 2.236067977 for the golden mean
z = ((p1 + 1)/2)/pixel:
z = z*z*z + pixel*((p1 + 1)/2),
|z| <= 4;
}
test3 {; Michael Theroux [71673,2767]
;fix and generalization by Ron Barnett [70153,1233]
;=phi
; try p1 = 2.236067977 for the golden mean
z = ((p1 + 1)/2)/pixel:
z = z*z + pixel*((p1 + 1)/2)/((p1 - 1)/2),
|z| <= 4;
}
testm {
; Try p1=0.25 and p2=0.15 with float=y or potential=255/800/255
z = 0, c=pixel:
z = sqr(z)+c,
c=c+(p1 * (|z| <= p2)),
|z| <= 4
}
TjerCGhalley (XYAXIS) {; Chris Green -- Halley's formula
; Modified by Tobey J. E. Reed [76437,375]
; P1 usually 1 to 1.5, P2 usually zero. Use floating point.
z=(1,1):
z5=z*z*z*z*z,
z6=z*z5, z7=z*z6,
z=z-p1*((z7-z+pixel)/ ((p1*z6-3)-(8.0*z5)*(z7+z-pixel)/(3.30*z6-12))),
0.0001 <= |z7-z-pixel|
}
TjerCubic (XYAXIS) {; Lee Skinner [75450,3631]
; Modified by Tobey J. E. Reed [76437,375]
p = pixel, test = p1 + 3,
t3 = 5*p, t2 = p*p,
a = (t2 + 1)/t3+t2, b = 3.149*a*a*a + (t2 - 5)/t2,
aa3 = a*a*p1, z = 0 - a :
z = z*z - aa3*z + a,
|z| < test
}
TjerDeltaLog(XAXIS) {; Mark Peterson
; Modified by Tobey J. E. Reed [76437,375]
z = pixel, c = log(pixel):
z = cosh(z) + c/2,
|z| <= 4
}
TjerDragon {; Mark Peterson
; Modified by Tobey J. E. Reed [76437,375]
z = Pixel:
z = tan(z) + (-0.74543, 0.2),
|z| <= 4
}
TjerEnt {; Scott Taylor
; Modified by Tobey J. E. Reed [76437,375]
; Try params=.5/.75 and the first function as exp.
; Zoom in on the swirls around the middle. There's a
; symmetrical area surrounded by an asymmetric area.
z = Pixel, y = fn1(z)+p1, base = log(p1):
z = y * 3.1416 * log(z)/base,
|z| <= 5
}
TjerFzppfnpo {; Lee Skinner [75450,3631]
; Modified by Tobey J. E. Reed [76437,375]
z = pixel, f = 2*(pixel)^(pixel):
z = fn1(z) + f,
|z| <= 50
}
TjerFzppfnre {; Lee Skinner [75450,3631]
; Modified by Tobey J. E. Reed [76437,375]
z = pixel, f = 1./(pixel):
z = fn1(z) + f * p1,
|z| <= 50
}
TjerHyperMandel {; Chris Green.
; Modified and Generalized by Tobey J. E. Reed [76437,375]
; A four dimensional version of the mandelbrot set.
; Use P1 to select which two-dimensional plane of the
; four dimensional set you wish to examine.
; Use floating point.
a=(0,0),b=(0,0):
z=z+1, anew=fn1(a)-fn1(b)+pixel,
b=3.17*a*b-p1, a=anew,
|a|+|b| <= 4
}
TjerInvMandel (XAXIS) {; Mark Peterson
; Modified by Tobey J. E. Reed [76437,375]
c = z = 1 / pixel:
z = cos(z) + 2*c;
|z| <= 4
}
TjerMandelTangent {; Fractal Creations example (revised for v.16)
; Modified by Tobey J. E. Reed [76437,375]
z = pixel:
z = pixel * tan(z) * 3.14159 * p1,
|real(z)| < 32
}
TjerMTet (XAXIS) {;Mandelbrot form 1 of the Tetration formula -- Lee Skinner
; Modified and Generalized by Tobey J. E. Reed [76437,375]
z = pixel:
z = (pixel ^ z + pixel) + fn1(pixel),
|z| <= (P1 + 3)
}
TjerNewton4(XYAXIS) {; Mark Peterson
; Modified by Tobey J. E. Reed [76437,375]
z = pixel, Root = 1:
z3 = z*z*z,
z4 = z3 * z,
z = (3 / z4 - Root) / (6 * z3),
.004 <= |z4 - Root|
}
TjerNewtonSinExp (XAXIS) {; Chris Green
; Generalized by Tobey J. E. Reed [76437,375]
; Newton's formula applied to sin(x)+exp(x)-1=0.
; Use floating point.
z=pixel:
z1=exp(z),
z2=sin(z)+z1-1,
z=z-p1*z2/(fn1(z)-z1),
.0001 < |z2|
}
TLog (XAXIS) = {; Lee Skinner [75450,3631]
z = c = log(pixel):
z = c ^ z,
z <= (p1 + 3)
}
Tobey3(XAXIS) = {
z = pixel:
c = pixel - sqr(z),
c = pixel + c/z,
z = c - z * pixel,
|z| < 4
}
TobeyCGNewton3 {; Chris Green -- A variation on newton iteration.
; Modified and Generalized by Tobey J. E. Reed [76437,375]
; The initial guess is fixed at (1,1), but the equation solved
; is different at each pixel ( x^3-pixel=0 is solved).
; Use floating point.
; Try P1=1.8.
z=(1,1):
z2=z*z, z3=z*z2,
z=z-p1*fn1((z2-pixel)/(2.13*z2)),
0.0001 < |z3-pixel|
}
TobeyHalley (XYAXIS) {; Chris Green. Halley's formula applied to x^7-x=0.
; Modified and Generalized by Tobey J. E. Reed [76437,375]
; P1 usually 1 to 1.5, P2 usually zero. Use floating point.
; Setting P1 to 1 creates the picture on page 277 of Pickover's book
z=pixel:
z5=z*z*z*z*z, z6=fn1(z*z5),
z7=fn2(z*z6),
z=fn2(z-p1*((z7-z))/ (fn1((7.0*z6-1)-(42.0*z5)*(z7-z)/(14.0*z6-2)))),
0.0001 <= |z7-z|
}
TobeyHalleySin (XYAXIS) {; Chris Green. Halley's formula applied to sin(x)=0.
; Generalized by Tobey J. E. Reed [76437,375]
; Use floating point.
; P1 = 0.1 will create the picture from page 281 of Pickover's book.
z=pixel:
s=fn1(z), c=fn2(z)
z=z+p1*(s/(c-(s-s)/(c*c))),
0.0001 <= |s|
}
TobeyLeeMandel1(XYAXIS) {; Kevin Lee
; Generalized by Tobey J. E. Reed [76437,375]
z=Pixel:
c=fn1(pixel)/z,
c=z+2*c,
z=fn2(z+1),
|z|<4
}
TobeyLeeMandel2(XYAXIS) {; Kevin Lee
; Generalized by Tobey J. E. Reed [76437,375]
z=Pixel:
c=fn1(pixel)/z,
c=z+c,
z=fn2(c*pixel),
|z|<4
}
TobeyLeeMandel3(XAXIS) {; Kevin Lee
; Generalized by Tobey J. E. Reed [76437,375]
z=Pixel, c=Pixel-fn1(z):
c=Pixel+c/z,
z=c-fn2(z*pixel),
|z|<4
}
TobeyMyFractal {; Fractal Creations example
; Generalized by Tobey J. E. Reed [76437,375]
c = z = 1/pixel:
z = fn1(z) + c/p1,
|z| <= 4
}
TobeyPsudoMandel(XAXIS) {; davisl - try center=0,0/magnification=28
; Generalized by Tobey J. E. Reed [76437,375]
z = Pixel:
z = ((z/2.7182818)^z)*fn1(6.2831853*z) + pixel,
|z| <= 4
}
TobeyRichard1 (XYAXIS) {; Jm Richard-Collard
; Generalized by Tobey J. E. Reed [76437,375]
z = pixel:
sq=z*z, z=(sq*fn1(sq)+sq)+pixel,
|z|<=50
}
TobeyRichard2 (XYAXIS) {; Jm Richard-Collard
; Generalized by Tobey J. E. Reed [76437,375]
z = pixel:
z=1/(fn1(z*z+pixel*pixel)),
|z|<=50
}
TobeyRichard3 (XAXIS) {; Jm Richard-Collard
; Generalized by Tobey J. E. Reed [76437,375]
z = pixel:
sh=fn1(z), z=(1/(sh*sh))+pixel,
|z|<=50
}
TobeySterling(XYAXIS) {; davisl
; Generalized by Tobey J. E. Reed [76437,375]
z = Pixel:
z = (fn1((z/2.7182818)^z))/fn2(6.2831853*z),
|z| <= 4
}
TobeySterling2(XAXIS) {; davisl
; Generalized by Tobey J. E. Reed [76437,375]
z = Pixel:
z = ((z/2.7182818)^z)/fn1(6.2831853*z) + pixel,
|z| <= 4
}
TobeyWineglass(XAXIS) {; Pieter Branderhorst
; Modified and Generalized by Tobey J. E. Reed [76437,375]
c = z = pixel:
z = z * z + c,
c = (1+flip(imag(fn1(c)))) * real(fn1(c)) / 3 + z,
|z| <= 4 }
TSinh (XAXIS) = {; Lee Skinner [75450,3631]
z = c = sinh(pixel):
z = c ^ z,
z <= (p1 + 3)
}
TurtleC(XAXIS_NOPARM)[float=y function=sqr/sqr] {; Jonathan Osuch
; Generalized by Tobey J. E. Reed [76437,375]
; Try p1=0, p2=4, fn1=sqr, fn2=sqr
; Note: use floating point
z = p1:
x = real(z),
IF (x < 0)
z = fn1(z) + pixel
ELSE
z = fn2(z) - pixel
ENDIF
|z| <= p2
}
ULI_1 = {; from ULI.FRM
z = Pixel:
z = fn1(1/fn2(z)),
|z| <= 4
}
ULI_2 = {; from ULI.FRM
z = Pixel:
z = fn1(1/fn2(z+p1)),
|z| <= p2
}
ULI_3 = {; from ULI.FRM
z = Pixel:
z = fn1(1/fn2(z+p1)+p1),
|z| <= p2
}
ULI_4 = {; from ULI.FRM
z = Pixel:
z = fn1(1/(z+p1))*fn2(z+p1),
|z| <= p2
}
ULI_5 = {; from ULI.FRM
z = Pixel, c = fn1(pixel):
z = fn2(1/(z+c))*fn3(z+c),
|z| <= p1
}
ULI_6 = {; from ULI.FRM
z = Pixel:
z = fn1(p1+z)*fn2(p2-z),
|z| <= p2+16
}
WaldoTwinsC(XAXIS_NOPARM)[float=y function=cosxx/sin] {; Jonathan Osuch
; Generalized by Tobey J. E. Reed [76437,375]
; Try p1=0, p2=4, fn1=cosxx, fn2=sin
; Note: use floating point
z = p1:
z = fn1(fn2(z+pixel)) + pixel,
|z| <= p2
}
Whatever_the_name(XAXIS) = {
z = pixel:
z=z*z+(1/z*z)+pixel,
}
z^3-1=0(XAXIS) {
; Advanced Fractal Programming in C - Stevens
; Run with inside = ZMAG to turn off periodicity checking
x=real(pixel), y=imag(pixel):
x2 = x*x, y2 = y*y,
xold = x, yold = y, xmy = x2 - y2,
d = 3 * (xmy * xmy + 4*x2*y2),
x = .66666667*x + xmy/d, y = .66666667*y - 2*x*y/d,
x != xold && y != yold
}
Ze2 (XAXIS) = {; Lee Skinner [75450,3631]
s1 = exp(1.,0.),
s = s1 * s1,
z = Pixel:
z = z ^ s + pixel,
|z| <= 100
}
Zexpe (XAXIS) = {; Lee Skinner [75450,3631]
s = exp(1.,0.), z = Pixel:
z = z ^ s + pixel,
|z| <= 100
}
Zexpe2 (XAXIS) = {; Lee Skinner [75450,3631]
s = exp(1.,0.), z = Pixel:
z = z ^ s + z ^ (s * pixel),
|z| <= 100
}
Zppchco8 {; Lee Skinner [75450,3631]
z = pixel, f = cosxx (pixel):
z = cosh (z) + f,
|z|<=8192
}