Your IP : 216.73.216.48
IslandOfChaos(XAXIS_NOPARM)[float=y function=sqr/sin/cosxx] {; Jonathan Osuch
; Generalized by Tobey J. E. Reed [76437,375]
; Try p1=0, p2=4, fn1=sqr, fn2=sin, fn3=cosxx
; Note: use floating point
z = p1, x = 1:
IF (x < 10)
z=fn1(z) + pixel
ELSE
z=fn2(z) / fn3(z) + pixel
ENDIF
x = x+1,
|z| <= p2
}
j1 {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2,
|z| <= 4
}
jc {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2*c,
|z| <= 4
}
jfnc {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2*fn1(c),
|z| <= 4
}
jfnz {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2*fn1(z),
|z| <= 4
}
JMask = {; Ron Barnett [70153,1233]
; try p1 = (1,0), p2 = (0,0.835), fn1 = sin, fn2 = sqr
z = fn1(pixel):
z = P1*fn2(z)^2 + P2, |z| <= 4
}
joc {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2/c,
|z| <= 4
}
joz {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2/z,
|z| <= 4
}
jz {; from EXPLOD.FRM
z=pixel, c=p1:
z=sqr(z)+c,
c=c+p2*z,
|z| <= 4
}
JSomethingelse (xyaxis) = {
z = pixel:
z = p1 * (z*z + 1/z/z),
|z| <= 1000000
}
J_Lagandre2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (3 * z*z - 1) / 2 + c
|z| < 100
}
J_Lagandre3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = z * (5 * z*z - 3) / 2 + c
|z| < 100
}
J_Lagandre4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z*z*(35 * z*z - 30) + 3) / 8 + c
|z| < 100
}
J_Lagandre5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = z* (z*z*(63 * z*z - 70) + 15 ) / 8 + c
|z| < 100
}
J_Lagandre6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z*z*(z*z*(231 * z*z - 315) + 105 ) - 5) / 16 + c
|z| < 100
}
J_Lagandre7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = z* (z*z*(z*z*(429 * z*z - 693) + 315) - 35 ) / 16 + c
|z| < 100
}
J_Laguerre2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z*(z - 4) +2 ) / 2 + c,
|z| < 100
}
J_Laguerre3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z*(z*(-z + 9) -18) + 6 ) / 6 + c,
|z| < 100
}
J_Laguerre4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z * ( z * ( z * ( z - 16)+ 72) - 96)+ 24 ) / 24 + c,
|z| < 100
}
J_Laguerre5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z * ( z * ( z * ( z * (-z +25) -200) +600) -600) + 120 ) / 120 + c,
|z| < 100
}
J_Laguerre6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = (z *(z *(z *(z *(z*(z -36) +450) -2400) + 5400)-4320)+ 720) / 720 + c,
|z| < 100
}
J_TchebychevC2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z-2),
|z|<100
}
J_TchebychevC3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z-3),
|z|<100
}
J_TchebychevC4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(z*z-4)+2),
|z|<100
}
J_TchebychevC5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(z*z-5)+5),
|z|<100
}
J_TchebychevC6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(z*z*(z*z-6)+9)-2),
|z|<100
}
J_TchebychevC7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(z*z*(z*z-7)+14)-7),
|z|<100
}
J_TchebychevS2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z-1),
|z|<100
}
J_TchebychevS3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z-2),
|z|<100
}
J_TchebychevS4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(z*z-3)+1),
|z|<100
}
J_TchebychevS5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(z*z-4)+3),
|z|<100
}
J_TchebychevS6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(z*z*(z*z-5)+6)-1),
|z|<100
}
J_TchebychevS7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(z*z*(z*z-6)+10)-4),
|z|<100
}
J_TchebychevT2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(2*z*z-1),
|z|<100
}
J_TchebychevT3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(4*z*z-3),
|z|<100
}
J_TchebychevT4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(8*z*z+8)+1),
|z|<100
}
J_TchebychevT5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*(z*z*(16*z*z-20)+5)),
|z|<100
}
J_TchebychevT6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(z*z*(32*z*z-48)+18)-1),
|z|<100
}
J_TchebychevT7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(z*z*(64*z*z-112)+56)-7),
|z|<100
}
J_TchebychevU2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(4*z*z-1),
|z|<100
}
J_TchebychevU3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(8*z*z-4),
|z|<100
}
J_TchebychevU4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(16*z*z-12)+1),
|z|<100
}
J_TchebychevU5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(32*z*z-32)+6),
|z|<100
}
J_TchebychevU6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*(z*z*(z*z*(64*z*z-80)+24)-1),
|z|<100
}
J_TchebychevU7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = pixel, z = P1:
z = c*z*(z*z*(z*z*(128*z*z-192)+80)-8),
|z|<100
}
JuliaConj(Origin) {; Paul J. Horn - a conjugate Julia (I think)
; try real part of p1 = -1.1 and imag part of p1 = .09
z = pixel:
z = Sqr(conj(z)) + P1,
|z| <= 4
}
JuliConj01(Origin) {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = -.93, imag(p1) = .3, map = blues
z = pixel:
z = Sqr(z) + Conj(P1),
|z| <= 4
}
JuliConj02(Origin) {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = .3, imag(p1) = .25, map = neon
z = pixel:
z = Sqr(Conj(z)) + Conj(P1),
|z| <= 4
}
JuliConj03 {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = .40, imag(p1) = 0, map = glasses2
z = pixel:
z = Sqr(conj(z))*conj(z) + P1,
|z| <= 4
}
JuliConj04 {; Paul J. Horn - a conjugate Julia (I think)
;Try real(p1) = .53, imag(p1) = .63, map = volcano
z = pixel:
z = Sqr(z)*z + Conj(P1),
|z| <= 4
}
JuliConj05 {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = .6, imag(p1) = .4, map = chroma
z = pixel:
z = Sqr(conj(z))*conj(z) + Conj(P1),
|z| <= 4
}
JuliConj06(Origin) {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = .99, imag(p1) = .72
z = pixel:
z = Sqr(Sqr((conj(z)))) + P1,
|z| <= 4
}
JuliConj07(Origin) {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = -.245, imag(p1) = .44, map = royal
z = pixel:
z = Sqr(Sqr(z)) + Conj(P1),
|z| <= 4
}
JuliConj08(Origin) {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = -1, imag(p1) = .11, map = blues
z = pixel:
z = Sqr(Sqr((conj(z)))) + Conj(P1),
|z| <= 4
}
JuliConj09 {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = -.677, imag(p1) = .333, real(p2) = 9, map = blues
z = pixel:
z = (conj(z))^P2 + P1,
|z| <= 4
}
JuliConj10 {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = .1005, imag(p1) = .68, real(p2) = 5, map = chroma
z = pixel:
z = (z)^P2 + Conj(P1),
|z| <= 4
}
JuliConj11 {; Paul J. Horn - a conjugate Julia (I think)
; Try real(p1) = -.37, imag(p1) = .6, real(p2) = 6, map = volcano
z = pixel:
z = (conj(z))^P2 + Conj(P1),
|z| <= 4
}
JulibrotSlice1 = {; Randy Hutson - 2D slice of 4D Julibrot
z = real(p1)+flip(imag(pixel)), c = real(pixel)+flip(imag(p1)):
z = sqr(z)+c,
LastSqr <= 4
}
LambdaPwr {; Ron Barnett [70153,1233]
; try p1 = (0.75,0.75), p2 = (2.5,0)
z = pixel:
z = p1*z*(1 - z^p2),
|z| <= 100
}
Leeze (XAXIS) = {; Lee Skinner [75450,3631]
s = exp(1.,0.), z = Pixel, f = Pixel ^ s:
z = cosxx (z) + f,
|z| <= 50
}
Liar1 { ; by Chuck Ebbert. [76306,1226]
; X: X is as true as Y
; Y: Y is as true as X is false
; Calculate new x and y values simultaneously.
; y(n+1)=abs((1-x(n) )-y(n) ), x(n+1)=1-abs(y(n)-x(n) )
z = pixel:
z = 1 - abs(imag(z)-real(z) ) + flip(1 - abs(1-real(z)-imag(z) ) ),
|z| <= 1
}
Liar2 { ; by Chuck Ebbert. [76306,1226]
; Same as Liar1 but uses sequential reasoning, calculating
; new y value using new x value.
; x(n+1) = 1 - abs(y(n)-x(n) );
; y(n+1) = 1 - abs((1-x(n+1) )-y(n) );
z = pixel:
x = 1 - abs(imag(z)-real(z)),
z = flip(1 - abs(1-real(x)-imag(z) ) ) + real(x),
|z| <= 1
}
M-SetInNewton(XAXIS) {; use float=yes
; jon horner 100112,1700, 12 feb 93
z = 0, c = pixel, cminusone = c-1:
oldz = z,
nm = 3*c-2*z*cminusone,
dn = 3*(3*z*z+cminusone),
z = nm/dn+2*z/3,
|(z-oldz)|>=|0.01|
}
m1 {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1,
|z| <= 4
}
MandelConj(XAXIS) {; Paul J. Horn , this was mentioned in Pickover's book
; Computers, Chaos, Patterns and Beauty. He didn't give the forumula, so
; I came up with this
z = c = Pixel:
z = Sqr(conj(z)) + Pixel,
|z| <= 4
}
MandConj01(XAXIS) {; Paul J. Horn, see MandelConj.
; This is a variation on a theme.
z = c = Pixel:
z = Sqr(z) + Conj(Pixel),
|z| <= 4
}
MandConj02(XAXIS) {; Paul J. Horn, see MandelConj.
; Another variation on the theme.
z = c = Pixel:
z = Sqr(Conj(z)) + Conj(Pixel),
|z| <= 4
}
MandConj03(XAXIS) {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = Sqr(conj(z))*conj(z) + Pixel,
|z| <= 4
}
MandConj04(XAXIS) {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = Sqr((z))*(z) + Conj(Pixel),
|z| <= 4
}
MandConj05(XAXIS) {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = Sqr(conj(z))*conj(z) + Conj(Pixel),
|z| <= 4
}
MandConj06(XAXIS) {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = Sqr(Sqr(conj(z))) + Pixel,
|z| <= 4
}
MandConj07(XAXIS) {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = Sqr(Sqr((z))) + Conj(Pixel),
|z| <= 4
}
MandConj08(XAXIS) {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = Sqr(Sqr(conj(z))) + Conj(Pixel),
|z| <= 4
}
MandConj09 {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = (conj(z))^p1 + Pixel,
|z| <= 4
}
MandConj10 {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = z^p1 + Conj(Pixel),
|z| <= 4
}
MandConj11 {; Paul J. Horn
; yet another variation on the theme
z = c = Pixel:
z = (conj(z))^p1 + Conj(Pixel),
|z| <= 4
}
MandellambdaPwr {; Ron Barnett [70153,1233]
; This provide a "map" for LambdaPwr
z = (1/(p1+1))^(1/p1):
z = pixel*z*(1 - z^p1),
|z| <= 100
}
Mask = {; Ron Barnett [70153,1233]
; try fn1 = log, fn2 = sinh, fn3 = cosh
;P1 = (0,1), P2 = (0,1)
;Use floating point
z = fn1(pixel):
z = P1*fn2(z)^2 + P2*fn3(z)^2 + pixel,
|z| <= 4
}
mc {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1*c,
|z| <= 4
}
mfnc {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1*fn1(c),
|z| <= 4
}
mfnz {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1*fn1(z),
|z| <= 4
}
Michaelbrot {; Michael Theroux [71673,2767]
; Fix and generalization by Ron Barnett [70153,1233]
; Try p1 = 2.236067977 for the golden mean
;based on Golden Mean
z = pixel:
z = sqr(z) + ((p1 + 1)/2),
|z| <= 4
}
moc {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1/c,
|z| <= 4
}
Mothra (XAXIS) { ; Ron Lewen, 76376,2567
; Remember Mothra, the giant Japanese-eating moth?
; Well... here he (she?) is as a fractal! ;
z=pixel:
z2=z*z, z3=z2*z, z4=z3*z,
a=z4*z + z3 + z + pixel, b=z4 + z2 + pixel,
z=b*b/a,
|real(z)| <= 100 || |imag(z)| <= 100
}
moz {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1/z,
|z| <= 4
}
mz {; from EXPLOD.FRM
z=0, c=pixel:
z=sqr(z)+c,
c=c+p1*z,
|z| <= 4
}
M_Lagandre2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (3 * z*z - 1) / 2 + c
|z| < 100
}
M_Lagandre3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = z * (5 * z*z - 3) / 2 + c
|z| < 100
}
M_Lagandre4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z*z*(35 * z*z - 30) + 3) / 8 + c
|z| < 100
}
M_Lagandre5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = z* (z*z*(63 * z*z - 70) + 15 ) / 8 + c
|z| < 100
}
M_Lagandre6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z*z*(z*z*(231 * z*z - 315) + 105 ) - 5) / 16 + c
|z| < 100
}
M_Lagandre7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = z* (z*z*(z*z*(429 * z*z - 693) + 315) - 35 ) / 16 + c
|z| < 100
}
M_Laguerre2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z*(z - 4) +2 ) / 2 + c,
|z| < 100
}
M_Laguerre3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z*(z*(-z + 9) -18) + 6 ) / 6 + c,
|z| < 100
}
M_Laguerre4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z * ( z * ( z * ( z - 16)+ 72) - 96)+ 24 ) / 24 + c,
|z| < 100
}
M_Laguerre5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z * ( z * ( z * ( z * (-z +25) -200) +600) -600) + 120 ) / 120 + c,
|z| < 100
}
M_Laguerre6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = (z *(z *(z *(z *(z*(z -36) +450) -2400) +5400) -4320) +720) / 720 + c,
|z| < 100
}
M_TchebychevC2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z-2),
|z|<100
}
M_TchebychevC3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z-3),
|z|<100
}
M_TchebychevC4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(z*z-4)+2),
|z|<100
}
M_TchebychevC5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(z*z-5)+5),
|z|<100
}
M_TchebychevC6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(z*z*(z*z-6)+9)-2),
|z|<100
}
M_TchebychevC7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(z*z*(z*z-7)+14)-7),
|z|<100
}
M_TchebychevS2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z-1),
|z|<100
}
M_TchebychevS3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z-2),
|z|<100
}
M_TchebychevS4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(z*z-3)+1),
|z|<100
}
M_TchebychevS5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(z*z-4)+3),
|z|<100
}
M_TchebychevS6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(z*z*(z*z-5)+6)-1),
|z|<100
}
M_TchebychevS7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(z*z*(z*z-6)+10)-4),
|z|<100
}
M_TchebychevT2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(2*z*z-1),
|z|<100
}
M_TchebychevT3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(4*z*z-3),
|z|<100
}
M_TchebychevT4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(8*z*z+8)+1),
|z|<100
}
M_TchebychevT5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*(z*z*(16*z*z-20)+5)),
|z|<100
}
M_TchebychevT6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(z*z*(32*z*z-48)+18)-1),
|z|<100
}
M_TchebychevT7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(z*z*(64*z*z-112)+56)-7),
|z|<100
}
M_TchebychevU2 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(4*z*z-1),
|z|<100
}
M_TchebychevU3 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(8*z*z-4),
|z|<100
}
M_TchebychevU4 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(16*z*z-12)+1),
|z|<100
}
M_TchebychevU5 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(32*z*z-32)+6),
|z|<100
}
M_TchebychevU6 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*(z*z*(z*z*(64*z*z-80)+24)-1),
|z|<100
}
M_TchebychevU7 {; Rob den Braasem [rdb@KTIBV.UUCP]
c = P1, z = Pixel:
z = c*z*(z*z*(z*z*(128*z*z-192)+80)-8),
|z|<100
}
Natura {; Michael Theroux [71673,2767]
; Fix and generalization by Ron Barnett [70153,1233]
;phi yoni
; try p1 = 2.236067977 for the golden mean
z = pixel:
z = z*z*z + ((p1 + 1)/2)
|z| <= 4
}
Newducks(XAXIS) = {
z=pixel,t=1+pixel:
z=sqr(z)+t,
|z|<=4
}
non-conformal {; Richard Hughes (Brainy Smurf) [70461,3272]
; From Media Magic Calender - August
z=x=y=x2=y2=0:
t = x * y,
x = x2 + t + real(pixel), y = y2 - t + imag(pixel),
x2 = sqr(x), y2 = sqr(y), z=x + flip(y),
|z| <= 4
}
No_name(xaxis) = {
z = pixel:
z=z+z*z+(1/z*z)+pixel,
|z| <= 4
}
OldCGNewtonSinExp (XAXIS) {; Chris Green
; For images using old incorrect cos function
; Use floating point.
z=pixel:
z1=exp(z),
z2=sin(z)+z1-z,
z=z-p1*z2/(cosxx(z)+z1),
.0001 < |z2|
}
OldHalleySin (XYAXIS) {; Chris Green
; For images using old incorrect cos function
; Use floating point.
z=pixel:
s=sin(z),
c=cosxx(z),
z=z-p1*(s/(c-(s*s)/(c+c))),
0.0001 <= |s|
}
OldManowar (XAXIS) {; Lee Skinner [75450,3631]
z0 = 0, z1 = 0, test = p1 + 3, c = pixel :
z = z1*z1 + z0 + c,
z0 = z1,
z1 = z,
|z| < test
}
OldNewtonSinExp (XAXIS) {; Chris Green
; Newton's formula applied to sin(x)+exp(x)-1=0.
; For images using old incorrect cos function
; Use floating point.
z=pixel:
z1=exp(z), z2=sin(z)+z1-1
z=z-p1*z2/(cosxx(z)+z1),
.0001 < |z2|
}
phoenix_j (XAXIS) {; Richard Hughes (Brainy Smurf) [70461,3272]
; Use P1=0.56667/-0.5 & .1/.8
; Use floating point.
x=real(pixel), y=imag(pixel), z=nx=ny=x1=x2=y1=y2=0:
x2 = sqr(x), y2 = sqr(y),
x1 = x2 - y2 + real(p1) + imag(p1) * nx,
y1 = 2 * x * y + imag(p1) * ny,
nx=x, ny=y, x=x1, y=y1, z=nx + flip(ny),
|z| <= 4
}
phoenix_m {; Richard Hughes (Brainy Smurf) [70461,3272]
; Mandelbrot style map of the Phoenix curves
; Use floating point.
z=x=y=nx=ny=x1=y1=x2=y2=0:
x2 = sqr(x), y2 = sqr(y),
x1 = x2 - y2 + real(pixel) + imag(pixel) * nx,
y1 = 2 * x * y + imag(pixel) * ny,
nx=x, ny=y, x=x1, y=y1, z=x + flip(y),
|z| <= 4
}
PolyGen = {; Ron Barnett [70153,1233]
;p1 must not be zero
;zero can be simulated with a small
;value for p1
;use floating point
;try p1 = 1 and p2 = 0.3
z=(-p2+(p2*p2+(1-pixel)*3*p1)^0.5)/(3*p1):
z=p1*z*z*z+p2*z*z+(pixel-1)*z-pixel,
|z| <= 100
}
PseudoLambda {; Ron Barnett [70153,1233]
; Use floating point.
; try p1 = (-1,0.45), p2 = (1,0)
z = pixel:
x = real(z), y = imag(z),
x1 = -p1*(x - x*x + y*y) + p2,
y = -p1*(y - 2*x*y),
z = x1 + flip(y),
|z| <= 100
}
PseudoMandelLambda {; Ron Barnett [70153,1233]
; Use floating point.
z = 0.5, c = pixel:
x = real(z), y = imag(z),
x1 = -c*(x - x*x + y*y) + p1,
y = -c*(y - 2*x*y),
z = x1 + flip(y),
|z| <= 100
}
PseudoZeePi = {; Ron Barnett [70153,1233]
; try p1 = 0.1, p2 = 0.39
z = pixel:
x = 1-z^p1;
z = z*((1-x)/(1+x))^(1/p1) + p2,
|z| <= 4
}
Ramanujan1(ORIGIN) = {
z = pixel:
z = (cosh(p1 * sqr(z)) - sinh(p2 * sqr(z))/(p2 * sqr(z)))/z,
|z|<= 4
}
Raphaelbrot {; Michael Theroux [71673,2767]
; Fix and generalization by Ron Barnett [70153,1233]
;phi
; try p1 = 2.236067977 for the golden mean
z = pixel:
z = sqr(z) + ((p1 - 1)/2)
|z| <= 4
}
RCL_1 (XAXIS) { ; Ron Lewen [76376,2567]
; An interesting Biomorph inspired by Pickover's
; Computers, Pattern, Choas and Beauty.
; Use Floating Point
z=pixel:
z=pixel/z-z^2,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_11 { ; Ron Lewen, 76376,2567
; A variation on the formula used to generate
; Figure 9.18 (p. 134) from Pickover's book.
; P1 sets the initial value for z.
; Try p1=.75, or p1=2, or just experiment!
z=real(p1):
z=z*pixel-pixel/sqr(z)
z=flip(z),
abs(z) < 8
}
RCL_2 (XAXIS) { ; Ron Lewen [76376,2567]
; A biomorph flower? Simply a change in initial
; conditions from RCL_1 above
; Use Floating Point
z=1/pixel:
z=pixel/z-z^2
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_3 (XAXIS) { ; Ron Lewen [76376,2567]
; A seemingly endless vertical pattern. The most activity
; is around the center of the image.
; Use Floating Point
z=pixel:
z=pixel^z+z^pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_4_M (XAXIS) { ; Ron Lewen, 76376,2567
; A Mandelbrot-style variation on Pickover's book,
; Figure 8.9 (p. 105).
; Use floating point
z=pixel:
z=sin(z^2) + sin(z) + sin(pixel),
|z| <= 4
}
RCL_4_J { ; Ron Lewen, 76376,2567
; A julia-style variation of the formula in Figure 8.9
; (p. 105) of Pickover's book.
z=pixel:
z=sin(z^2) + sin(z) + sin(p1),
|z| <= 4
}
RCL_5_M (XAXIS) { Ron Lewen, 76376,2567
; A variation on the classical Mandelbrot set
; formula.
; Use floating point
z=pixel:
z=sin(z^2+pixel),
|z| <= 4
}
RCL_5_J (ORIGIN) { Ron Lewen, 76376,2567
; A variation on the classical Julia set.
; Use floating point
z=pixel:
z=sin(z^2+p1),
|z| <= 4
}
RCL_6_M (XAXIS) { ; Ron Lewen, 76376,2567
; A variation on the classic Mandelbrot formula
; Use floating point
z=pixel:
z=sin(z)^2 + pixel,
|z| <= 4
}
RCL_6_J (ORIGIN) { ; Ron Lewen, 76376,2567
; A variation on the classic Julia formula
; use floating point
z=pixel:
z=sin(z)^2 + p1,
|z| <= 4
}
RCL_7 (XAXIS) { ; Ron Lewen, 76376,2567
; Inspired by the Spider
; fractal type included with Fractint
z=c=pixel:
z=z^2+pixel+c
c=c^2+pixel+z
|z| <= 4
}
RCL_8_M { ; Ron Lewen, 76376,2567
; Another variation on the classic Mandelbrot
; set.
z=pixel:
z=z^2+flip(pixel)
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_8_J (ORIGIN) { ; Ron Lewen, 76376,2567
z=pixel:
z=z^2+flip(p1)
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_9 (XAXIS) { ; Ron Lewen, 76376,2567
z=pixel:
z=(z^2+pixel)/(pixel^2+z)
|z| <= 4
}
RCL_10 { ; Ron Lewen, 76376,2567
z=pixel:
z=flip((z^2+pixel)/(pixel^2+z))
|z| <= 4
}
RCL_12 (XAXIS) { ; Ron Lewen, 76376,2567
z=pixel:
z=(z^2+3z+pixel)/(z^2-3z-pixel)
|z| <= 10
}
RCL_13 (XAXIS) { ; Ron Lewen, 76376,2567
z=pixel:
z=(z^2+2z+pixel)/(z^2-2z+pixel)
|z| <= 100
}
RCL_14 (XAXIS) { ; Ron Lewen, 76376,2567
z=pixel:
z=z^pixel+pixel^z
|z| <= 96
}
RCL_15 (XAXIS) { ; Ron Lewen, 76376,2567
; Adapted from Pickover's Biomorph Zoo Collection in
; Figure 8.7 (p. 102).
z=pixel:
z=z^2.71828 + pixel,
|real(z)| <= 100 || |imag(z)| <= 100
}
RCL_16 (XAXIS) { ; Ron Lewen, 76376,2567
; Set fn1 to sqr to generate 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/fn1(z),
abs(z) < 8
}
RCL_Cosh (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_Cosh_Flip (XAXIS) { ; Ron Lewen, 76376,2567
; A FLIPed version of RCL_Cosh.
; An interesting repeating pattern with lots
; of detail.
; Use floating point
z=0:
z=flip(cosh(z) + pixel),
abs(z) < 40
}
RCL_Cosh_J { ; Ron Lewen, 76376,2567
; A julia-style version of RCL_Cosh above.
; Lots of interesting detail to zoom in on.
; Use floating point
z=pixel:
z=cosh(z) + p1,
abs(z) < 40
}
RCL_Cross1 { ; Ron Lewen, 76376,2567
; Try p1=(0,1), fn1=sin and fn2=sqr. Set corners at
; -10/10/-7.5/7.5 to see a cross shape. The larger
; lakes at the center of the cross have good detail
; to zoom in on.
; Use floating point.
z=pixel:
z=p1*fn1(fn2(z+p1)),
|z| <= 4
}
RCL_Cross2 { ; Ron Lewen, 76376,2567
; Try p1=(0,1), fn1=sin and fn2=sqr. Set corners at
; -10/10/-7.5/7.5 to see a deformed cross shape.
; The larger lakes at the center of the cross have
; good detail to zoom in on.
; Try corner=-1.58172/.976279/-1.21088/-.756799 to see
; a deformed mandelbrot set.
; Use floating point.
z=pixel:
z=pixel*fn1(fn2(z+p1)),
|z| <= 4
}
RCL_Logistic_1 (XAXIS) { ; Ron Lewen, 76376,2567
; Based on logistic equation x -> c(x)(1-x) used
; to model animal populations. Try p1=(3,0.1) to
; see a family of spiders out for a walk <G>!
z=pixel:
z=p1*z*(1-z),
|z| <= 1
}
RCL_Mandel (XAXIS) { ; Ron Lewen, 76376,2567
; The traditional Mandelbrot formula with a different
; escape condition. Try p1=(1,0). This is basically the M-Set
; with more chaos outside. p1=(0,0) yields a distorted M-set.
; Use floating point
z=pixel:
z=sqr(z) + pixel,
sin(z) <= p1
}