David Lowenstein wrote:
how does one calculate the rudy set?
David, that's what I've got (see below). Additional notes: RudySetPlus(Minus) - calculates the set for only one critical point (plus: z = a, minus: z = -a). RudySetOr - both critical points are used, pixel is considered "inside" if at least one of the crit. points remains bounded. This results in the union of RudySetPlus and RudySetMinus. RudySetAnd - both critical points are used, pixel is conidered "inside" only if both crit. points remain bounded. The result is the intersection of RudySetPlus and RudySetMinus. (Don't forget to set periodicity to 0 for the And/Or-types!) Regards, Gerald -------------------- Fractint formulas ------------------------ comment { Rudy Rucker's Parametrization of the Cubic Connectedness Locus for z^3 - 3*a^2*z + b with either: a = b = x + i*y or: a = x + i*x, b = y + i*y The original ( RudySetAnd ) is one of the fractal types in "James Gleick's Chaos - The Software" by Autodesk } RudySetPlus {;Rudy Rucker's CCL-Parametrization ( z = a ) ;Types: a = b = Pixel / a = (x,x), b = (y,y) ;----------------------------- ;p1 real: Bailout ;p1 imag: Type (choose 0 or 1) ;----------------------------- IF (imag(p1)) z = real(pixel)*(1,1), a = 3*sqr(z), b = imag(pixel)*(1,1) ELSE z = b = pixel, a = 3*sqr(z) ENDIF : z = z*(sqr(z)-a) + b p1 >= |z| } RudySetMinus {;Rudy Rucker's CCL-Parametrization ( z = -a ) ;Types: a = b = Pixel / a = (x,x), b = (y,y) :----------------------------- ;p1 real: Bailout ;p1 imag: Type (choose 0 or 1) ;----------------------------- IF (imag(p1)) z = real(pixel)*(-1,-1), a = 3*sqr(z), b = imag(pixel)*(1,1) ELSE b = pixel, a = 3*sqr(b), z = -b ENDIF : z = z*(sqr(z)-a) + b p1 >= |z| } RudySetOr {;Rudy Rucker's CCL-Parametrization ( Union ) ;Types: a = b = Pixel / a = (x,x), b = (y,y) ;periodicity=no ;----------------------------- ;p1 real: Bailout ;p1 imag: Type (choose 0 or 1) ;----------------------------- IF (imag(p1)) z1 = real(pixel)*(1,1), z2 = -z1 a = 3*sqr(z1), b = imag(pixel)*(1,1) ELSE z1 = b = pixel, z2 = -z1, a = 3*sqr(z1) ENDIF z = bail1 = bail2 = 0: IF (bail1 == 0) z1 = z1*(sqr(z1)-a) + b IF (p1 < |z1|) z = z1, bail1 = 1 ENDIF ENDIF IF (bail2 == 0) z2 = z2*(sqr(z2)-a) + b IF (p1 < |z2|) z = z2, bail2 = 1 ENDIF ENDIF bail1 == 0 || bail2 == 0 } RudySetAnd {;Rudy Rucker's CCL-Parametrization ( Intersection ) ;Typen: a = b = Pixel / a = (x,x), b = (y,y) ;periodicity=no ;----------------------------- ;p1 real: Bailout ;p1 imag: Type (choose 0 or 1) ;----------------------------- IF (imag(p1)) z1 = real(pixel)*(1,1), z2 = -z1 a = 3*sqr(z1), b = imag(pixel)*(1,1) ELSE z1 = b = pixel, z2 = -z1, a = 3*sqr(z1) ENDIF z = exit = 0: z1 = z1*(sqr(z1)-a) + b z2 = z2*(sqr(z2)-a) + b IF (p1 < |z1|) z = z1, exit = 1 ENDIF IF (p1 < |z2|) z = z2, exit = 1 ENDIF exit == 0 } ------------------- End of Fractint formulas ------------------