comment { Carr2100.ufm Version 1.2 Ultra Fractal conversions of Robert Carr's formulas Carr2100 - Carr2199 by Erik Reckase / Lale Erguner, 12 December 2002 History: Version 1.3 - Fixes for UF3 compatibility by Lale Erguner Version 1.2 - Minor fixes, eliminated divide by zero Version 1.1 - Major optimization overhaul, cleanup, hints Version 1.0 - Initial Release Original formulas pulled from _rc2.frm Fixed errors in Carr 2185, 2186, 2187 } Carr2100 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. [101324,3444],1996 init: c=(-.7456,-.13) z=conj(tan(pixel))-sqr(conj(.1/pixel))-sqr(flip(.02/pixel)) z1 = 1.5*z, z2 = 2.25*z, z3 = 3.375*z, z4 = 5.0625*z l1=round(real(p1)), l2=round(imag(p1)) l3=round(real(p2)), l4=round(imag(p2)) float bailout=16, int iter=0 loop: IF (iter==l1) z=c=z1 ELSEIF (iter==l2) z=c=z2 ELSEIF (iter==l3) z=c=z3 ELSEIF (iter==l4) z=c=z4 ENDIF z=z*z+c iter=iter+1 bailout: |real(z)| <= bailout default: title = "Carr 2100" periodicity = 0 maxiter = 500 magn = 1.1 center = (0,0) method = multipass param p1 caption = "Iter Limits 1,2" default = (100,150) hint = "0< Re(P1) < Im(P1) < Re(P2) < Im(P2) =limit) c = (-.743380900000982,-.131850030300002) ENDIF z=z*z+c compt=compt+1 bailout: |z|<=bailout default: title = "Carr 2103" periodicity = 0 maxiter = 500 magn = 1.3 center = (-.2,0) method = multipass param p1 caption = "Iter Limit" default = (100,0) hint = "This iteration limit is scaled by the cosine of \ the current pixel divided by 5. The real part of \ this scaled iteration limit signals a change in the \ value of c." endparam } Carr2104 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=flip(1-pixel)*sqr(pixel)-conj(.1/pixel)-flip(.01/pixel) c=(-.8006,-.149), int iter = 1, rad = 6, center = (1,.1) pix = (10*pixel+(8,-5))*(-.1,-.95) zn = center+rad/(pix-center), int limit = round(real(p1)) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = .0001 loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = 0 ENDIF float zfinal = |z| float bfinal = b1 ELSE IF (z==0) z1 = 0 ELSE z1 = (z^5-1)/(4*z^4) ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter+1 bailout: zfinal <= bfinal default: title = "Carr 2104" periodicity = 0 maxiter = 500 magn = 1.2 center = (.25,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2105 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=flip(1+pixel)*sqr(conj(pixel))-conj(.1/pixel)+flip(.01/pixel) c=(-.63,-.4), int iter = 1, rad = 6, center = (1,.1) pix = (10*pixel+(8,-5))*(-.1,-.95) zn = center+rad/(pix-center), int limit = round(real(p1)) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = .0001 loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = 0 ENDIF float zfinal = |z| float bfinal = b1 ELSE IF (z==0) z1 = 0 ELSE z1 = (z^5-1)/(4*z^4) ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter+1 bailout: zfinal <= bfinal default: title = "Carr 2105" periodicity = 0 maxiter = 500 magn = 1.2 center = (-.3,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2106 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=c=pixel-2/(sinh(0.10/pixel)-sqr(tanh(0.010/pixel))) float iter = 1, rad = 6, center = (1,.1) pix = (10*pixel+(8,-5))*(-.1,-.95) zn = center+rad/(pix-center), float limit = real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = .0001 loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4) ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter+1.2 bailout: zfinal <= bfinal default: title = "Carr 2106" periodicity = 0 maxiter = 500 magn = 16 center = (.025,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2107 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. [101324,3444],1996 init: c=(-.8006,-.149) z=pixel-1/(sinh(.1/pixel)-sqr(cosh(.025/pixel))) z1 = 1.5*z, z2 = 2.25*z, z3 = 3.375*z, z4 = 5.0625*z float l1=real(p1), float l2=imag(p1) float l3=real(p2), float l4=imag(p2) float bailout=16, float iter=0 loop: IF (iter==l1) z=c=z1 ELSEIF (iter==l2) z=c=z2 ELSEIF (iter==l3) z=c=z3 ELSEIF (iter==l4) z=c=z4 ENDIF z=z*z+c iter=iter+.75 bailout: |real(z)| <= bailout default: title = "Carr 2107" periodicity = 0 maxiter = 500 magn = 1.35 center = (-1.05,0) method = multipass param p1 caption = "Iter Limits 1,2" default = (100,150) hint = "0< Re(P1) < Im(P1) < Re(P2) < Im(P2) b1) ENDIF IF test3 && test0 z = 0 ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4) ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter+1.2 bailout: zfinal <= bfinal default: title = "Carr 2108" periodicity = 0 maxiter = 500 magn = 10 center = (0,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2109 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: c=(-.8006,-.149) z=pixel-(atan(.1/pixel)-sqr(acos(.025/pixel)))^-6 float iter = 1, rad = 6, center = (1,.1) pix = (10*pixel+(8,-5))*(-.1,-.95) zn = center+rad/(pix-center), float limit = real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = .0001 loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = 0 ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4) ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter+1.099 bailout: zfinal <= bfinal default: title = "Carr 2109" periodicity = 0 maxiter = 500 magn = 1.2 center = (0,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2110 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. [101324,3444],1996 init: c=(-.8006,-.149), p01=.1/pixel z=pixel-1/log(p01)-cos(p01+1.25)+conj(p01) z1=1.5*z, z2=2.25*z, z3=3.375*z, z4=5.0625*z l1=round(real(p1)), l2=round(imag(p1)) l3=round(real(p2)), l4=round(imag(p2)) float bailout=16, int iter=0 loop: IF (iter==l1) z=c=z1 ELSEIF (iter==l2) z=c=z2 ELSEIF (iter==l3) z=c=z3 ELSEIF (iter==l4) z=c=z4 ENDIF z=z*z+c iter=iter+1 bailout: |real(z)| <= bailout default: title = "Carr 2110" periodicity = 0 maxiter = 500 magn = 1.35 center = (0,0) method = multipass param p1 caption = "Iter Limits 1,2" default = (100,150) hint = "0< Re(P1) < Im(P1) < Re(P2) < Im(P2) b1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 + d2 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + 1.2 bailout: zfinal <= bfinal default: title = "Carr 2155" periodicity = 0 maxiter = 500 magn = 1.2 center = (0,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2156 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=flip(conj(abs(log(pixel)*sqrt(pixel)))) c=sin((-.85126,.139)) float iter=1, rad=6, center=(-3.6,-3) pix=(10*pixel+(5,-3.5))*(-.1,-.95) zn=flip(center+rad/(pix-center)), float limit=real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = 0.0001 d1=-conj(.0005455/pixel), d2=sqr(d1) loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 + d2 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + 1.2 bailout: zfinal <= bfinal default: title = "Carr 2156" periodicity = 0 maxiter = 500 magn = 1 center = (.9,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2157 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=c=pixel-(tanh(.25/pixel)-sqr(sinh(.0125/pixel)))^-6 float iter=1, rad=6, center=(-7.6,-3) pix=(10*sqr(pixel)+(5,-3.5))*(-.1,-.95) zn=center+rad/(pix-center), float limit=real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = 0.0001 d1=conj(.0005455/pixel) loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + 1.099 bailout: zfinal <= bfinal default: title = "Carr 2157" periodicity = 0 maxiter = 500 magn = 4 center = (0,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2158 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: p0=1/pixel, c=conj(pixel)/(flip(p0)-conj(p0)) z=p0/(3*pixel-flip(p0)-conj(p0)) float iter=1, rad=6, center=(-7.6,-3) pix=(10*sqr(pixel)+(5,-3.5))*(-.1,-.95) zn=center+rad/(pix-center), float limit=real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = 0.0001 d1=conj(.0005455/pixel) loop: test0 = !test0 IF (iter!=limit) z = conj(z-zn) + conj(zn) ELSE z = conj(zn) ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + 2.099 bailout: zfinal <= bfinal default: title = "Carr 2158" periodicity = 0 maxiter = 500 magn = 1 center = (0,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2159 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=flip(1-pixel)^1.8/flip(asinh(pixel+1.5)), c=(-.3,-.625) float iter=1, rad=6, center=(-7.6,-3.0) pix=(10*sqr(pixel)+(5.0,-3.5))*(-0.1,-0.95) zn=center+rad/(pix-center), float limit=real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = 0.0001, d1=conj(.00054550/pixel) loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + 2.099 bailout: zfinal <= bfinal default: title = "Carr 2159" periodicity = 0 maxiter = 500 magn = .8 center = (1.1,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2160 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: c=(-.7456,-.132) z=log((pixel+4/pixel)^1.8)*asin(1-pixel) float iter=1, rad=6, center=(-7.6,-3) pix=(10*sqr(pixel)+(5,-3.5))*(-.1,-.95) zn=center+rad/(pix-center), float limit=real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = .0001, d1=conj(.00054550/pixel) loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + .099 bailout: zfinal <= bfinal default: title = "Carr 2160" periodicity = 0 maxiter = 500 magn = 4 center = (1.07,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2161 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. init: z=c=pixel*tanh(conj(.9/pixel)) float iter=1, rad=6, center=(-7.6,-3) pix=(10*sqr(pixel)+(5,-3.5))*(-.1,-.95) zn=center+rad/(pix-center), limit=real(p1) bool test0 = TRUE, bool test3 = FALSE float b1 = 16, float b2 = .0001, d1=conj(.00054550/pixel) loop: test0 = !test0 IF (iter==limit) z = zn ENDIF IF (iterb1) ENDIF IF test3 && test0 z = (0,0) ENDIF float zfinal = |z| float bfinal = b1 ELSE IF z==0 z1 = 0 ELSE z1 = (z^5-1)/(4*z^4)+d1 ENDIF z = z - z1 float bfinal = |z1| float zfinal = b2 ENDIF iter = iter + 2.099 bailout: zfinal <= bfinal default: title = "Carr 2161" periodicity = 0 maxiter = 500 magn = 2 center = (0,0) method = multipass param p1 caption = "Iteration Limit" default = (100,0) hint = "The real part of this parameter signifies the point \ at which the iterating formula changes. The imag \ part is not used, but remains for Fractint compat." endparam } Carr2162 {; Updated for UF2 by Erik Reckase, March 2000 ; Modified Sylvie Gallet frm. [101324,3444],1996 init: c=pixel, z=1/(2*pixel+flip(1/pixel)-conj(1/pixel)) d1=conj(.00000455/pixel), d4 = 4*d1 z1=1.5*z+d1, z2=2.25*z+d1, z3=3.375*z+d1, z4=11.0625*z+d1 l1=round(real(p1)), l2=round(imag(p1)) l3=round(real(p2)), l4=round(imag(p2)) float bailout=16, int iter=0 loop: IF (iter==l1) z=c=z1 ELSEIF (iter==l2) z=c=z2 ELSEIF (iter==l3) z=c=z3 ELSEIF (iter==l4) z=c=z4 ENDIF c = c + d4 z=(z+d4)^2+c iter=iter+1 bailout: |real(z)| <= bailout default: title = "Carr 2162" periodicity = 0 maxiter = 500 magn = 1.2 center = (-0.5,0) method = multipass param p1 caption = "Iter Limits 1,2" default = (100,150) hint = "0< Re(P1) < Im(P1) < Re(P2) < Im(P2)