{ ======================================================================== } { File originally distributed with FRAC'Cetera Vol 2 Iss 7 } {========================================================================== = Compiled by Jon Horner for FRAC'Cetera from several sources - Jul 93 = = F'names, where present, represent FRAC'Cetera created variations or = = derivatives based, often quite loosely, on the author's originals. = ==========================================================================} { IKENAGA - Formula originally discovered by Bruce Ikenaga, at Western Reserve University, Indiana. Documented in Dewdney's `Armchair Universe". The Ikenaga set is: Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C where: Z(n) = x + yi and C = a + bi In Basic (with Mandelbrot for comparison): Mandelbrot: Ikenaga: newX = x*x - y*y + a newX = x*x*x - 3*x*y*y + a*x - b*y - x - a newY = 2*x*y + b newY = 3*x*x*y - y*y*y + a*y + b*x - y - b Ikenaga is also in R.F.J. Stewart's MANDPLOT; Larry Cobb's DRAGONS4; Mike Curnow's !Fractal for the Archimedes, and Tim Harris's CAL. ==========================================================================} !_Press_F2_! {; There is text in this formula file. Shell to DOS with ; the key and use a text reader to browse the file. } Ikenaga(XAXIS) { ; this version correct per Roderick Stewart - ; announcement in Fractal Report 25 p2. ; same as letter, Joyce Haslam Mar 1993 ; z=z*z*z+ (c-1)*z-c produces same results. z = (0,0), c = pixel : z = z * z * z + z * (c-1) - c , |z|<=4 } IkenagaJ.1(XAXIS) { ; this version correct per Roderick Stewart - ; announcement in Fractal Report 25 p2. ; same as letter, Joyce Haslam Mar 1993 ; z=z*z*z+ (c-1)*z-c produces same results. z = (0,0), c = pixel : z = z * (z * z + (c-1)) - c , |z|<=4 } IkenagaJUL { ; formula from a letter from Joyce Haslam Mar 1993. ; Asymmetric. try p1 = (0.56667, 0.36) ; Next line, from Haslam article Fractal Report 24 p5 ; z=z*z*z+ (c-1)*z-c produces same results. ; Same as Julike in REB001.FRM z = pixel, c = p1 : z = z * z * z + z * (c-1) - c , |z| <= 4 } IkenagaJULJ.1 { ; formula from a letter from Joyce Haslam Mar 1993. ; Asymmetric. try p1 = (0.56667, 0.36) ; Next line, from Haslam article Fractal Report 24 p5 ; z=z*z*z+ (c-1)*z-c produces same results. ; Same as Julike in REB001.FRM z = pixel, c = p1 : z = z * (z * z + (c-1)) - c , |z| <= 4 } { The rest are all variations on the two basic formulas } IkenagaPwr(XAXIS) { ; from Jon Horner z = (0,0), c = pixel : z = z * z * z + z * (c-1) - c ^ p1 , z| <=4 } IkenagaPwrJul { ; from Jon Horner - asymmetric ; try p1 = (0.035, -0.35), p2 = 2 z = pixel, c = p1 : z = z * z * z + z * (c-1) - c ^ p2 , |z| <=4 } Ikenaga4(XAXIS) { ; CAL v3.8 calls it Ikenaga-4Set ; Per Haslam, Fractal Report 25 p2 (IKE4) ; z^4 is used instead of z^3 and multiplication ; is used in place of addition. z = (0,0), c = pixel: z = z * z * z * z * (c-1) - c , |z|<= 4 } Ikenaga4JUL(ORIGIN) { ; Jon Horner, from IKE4 - Fractal Report 25 p2 ; try p1 = (0.3874, 0.85) z = pixel, c = p1 : z = z * z * z * z * (c-1) - c, |z| <= 4 } IkenagaABS(XAXIS) { ; Jon Horner ; Ikenaga with alternative bailout z = (0,0), c = pixel : z = z * z * z + z * (c-1) - c , abs(z)<=4 } IkenagaABSJUL { ; Jon Horner ; IkenagaJul with alternative bailout z = pixel, c = p1 : z = z * z * z + z * (c-1) - c , abs(z) <= 4 } Ikenaga4BIO(XAXIS) { ; Ikenaga4 variation - Jon Horner ; float=y z = (0,0), c = pixel : z = z * z * z * z * (c-1) - c , |real(z)|<=4 || |imag(z)|<=4 } Ikenaga4BIOJUL(ORIGIN){ ; Jon Horner, from IKE4 - FR 25, p2 ; try p1 = (0.3874, 0.85) float=y z = pixel, c = p1 : z = z * z * z * z * (c-1) - c, |real(z)|<=4 || |imag(z)|<=4 } IkenagaFN(XAXIS) {; Jon Horner ; derived from Ikenaga z = (0,0), c = fn1(pixel) : z = z * z * z + z * (c-1) - c , |z| <=4 } IkenagaFNJUL { ; Jon Horner ; derived from IkenagaJul ; asymmetric: try p1 = (0.56667, 0.36) z = fn1(pixel), c = p1 : z = z * z * z + z * (c-1) - c, |z| <= 4 } IkenagaJUL1+(ORIGIN){ ; formula from an article by Joyce Haslam ; in Fractal Report 24 (w/+pixel stead of +c) ; symmetric z = pixel, c = p1 : z = z * z * z + (c-1) * z + pixel , |z|<=4 } Ikenaga2(XAXIS) { ; from Joyce Haslam article, Fractal Report Iss 24 p5. ; Uses pixel instead of c !!!! ; CAL v4.0 calls it UnamiSet. FR 25 calls it Unknown. ; CAL v4.0 IkenagaSet(XAXIS) = ; {z=0:z=z*z*z+z*(pixel-1)-pixel,|z|<=|2| z = pixel: z = z * z * z + (pixel-1) * z - pixel, |z|<=4 } IkenagaMap(XAXIS) {; from REB001.FRM - by Ron Barnett 70153,1233 ; The initial starting point allows the function to provide ; a "map" for the corresponding Julia (IkenagaJul) z = ((1-pixel)/3)^0.5: z = z*z*z + (pixel-1)*z - pixel, |z| <= 4 } IkeNewtMand { ; from REB001.FRM - by Ron Barnett 70153,1233 ; p1 > 0, < 2, float=yes z = c = pixel: zf = z*z*z + (c-1)*z - c; zd = 3*z*z + c-1; z = z - p1*zf/zd, 0.001 <= |zf| } IkeNewtJul { ; from REB001.FRM - by Ron Barnett 70153,1233 ; p1 > 0, < 2, float=yes z = pixel: zf = z*z*z + (p2-1)*z - p2; zd = 3*z*z + p2-1; z = z - p1*zf/zd, 0.001 <= |zf| } RecipIke { ; from REB001.FRM - by Ron Barnett 70153,1233 z = pixel: z = 1/(z*z*z + (p1-1)*z - p1), |z| <= 4 } F'FunctionIke { ; generalized by Jon Horner ; from RecipIke in REB001.FRM : - by Ron Barnett 70153,1233 z = pixel: z = fn1(z*z*z + (p1-1) * z - p1), |z| <= 4 } IkeGenM {; from REB002.FRM - by Ron Barnett 70153,1233 z = ((1-pixel)/(3*p1))^0.5: z =p1*z*z*z + (pixel-1)*z - pixel, |z| <= 100 } IkeGenJ {; from REB002.FRM - by Ron Barnett 70153,1233 z = pixel: z =p1*z*z*z + (p2-1)*z - p2, |z| <= 100 } IkeFrRbtGenM {; from REB002.FRM - by Ron Barnett 70153,1233 z = 2*(1-pixel)/(3*p1): z = p1*z*z*z + (pixel-1)*z*z - pixel, |z| <= 100 } IkeFrRbtGenJ {; from REB002.FRM - by Ron Barnett 70153,1233 z = pixel: z = p1*z*z*z + (p2-1)*z*z - p2, |z| <= 100 }