John W.,
Nice to see new fractals here. First "Diode" and now the rather fiery "BH_CubicMan" Thanks guys.
Thank *you* for the positive feedback! I'll misappropriate your thread for the next part of my "should have posted this years ago" theme, if you don't mind :-) These are the rest of the Xavier Buff / Christian Henriksen cubic formula(s). Again, the .par sets are just for getting sensible parameter settings and image coordinates right away without having to grasp around in the dark (quite literally sometimes regarding fractal images), nothing more. Short info on the capital L and/or U appended to the Mandelbrot formula names: L --> Shows the Mset when varying the Lambda parameter (fixed for the formulas in the last post), while now keeping the other parameter constant. U --> Union of Critical Points (better should have been named Union of Msets of both Critical Points). The non-U Mset formulas consider a point as part of the set if *both* Crit. Points remain bounded, for the U-named ones a pixel is in the set if at least one Crit. Point remains finite. That's all. I hope you find interesting spots/images in there. (And I'll start my own thread for the next formula post, honest!) Regards, Gerald --------------------- Parameters and Formulas below --------------------------- BH_Julia {;Sample Julia Set, still in one piece ;-) ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenJul passes=t corners=-1.76207/1.038355/0.94650356/-0.55067558/-0.03527084/-1.3558952 params=1.25/-0.4/0.715/-0.715/16/0 float=y maxiter=512 inside=0 colors=@volcano.map } BH_CubicManL_1 {;Lambda plane ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=1.5628432/2.2234796/-0.24773864/0.24773864 params=0/0/1.5/0/16/0 float=y maxiter=1024 inside=0 periodicity=0 colors=@firestrm.map } BH_CubicManL_2 {;Lambda plane ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=1.691311038/1.676269023/0.1979422444/0.2087232275/1.680721041/0.\ 2120622409 params=0/0/1.5/0/16/0 float=y maxiter=1024 inside=0 periodicity=0 colors=@chroma.map } BH_CubicManL_2a {;Lambda plane ; reset=2002 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=1.6829595428/1.6820307298/0.2019951803/0.2064142184/1.6805040318\ /0.2052691949 params=0/0/1.5/0/16/0 float=y maxiter=2048 inside=0 periodicity=0 colors=@chroma.map } BH_CubicManL_3 {;Lambda plane ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=-1.3357339/-1.1135116/-0.083333333/0.083333333 params=0/0/0/1.5/16/0 float=y maxiter=1024 inside=0 periodicity=0 colors=@firestrm.map } BH_CubicManL_4 {;Lambda plane ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=-1.168193287/-1.152084382/-0.07006139885/-0.0886777812/-1.153458\ 218/-0.08970815761 params=0/0/0/1.5/16/0 float=y maxiter=2048 inside=0 periodicity=0 colors=@chroma.map } BH_CubicManL_5 {;Lambda plane ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=2.2224202/1.9147279/-0.20512821/0.20512821/1.9147279/0.20512821 params=0/0/1/0/16/0 float=y maxiter=512 inside=0 periodicity=0 colors=@volcano.map } BH_CubicManL_6 {;Lambda plane ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManL passes=t corners=0.5359977/2.111038/-0.59064/0.59064 params=0/0/0/1/16/0 float=y maxiter=512 inside=0 periodicity=0 colors=@volcano.map } BH_CubicManU_1 {;Union set of Critical Points ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManU corners=-2.033192/2.033192/2.710922/-2.710922/2.033192/-2.710922 params=0/0/-1.5125/0/900/0 float=y maxiter=2048 inside=0 periodicity=0 colors=000g00<3>d00c00c00<24>JDDIDDHEEGEE<2>FFF<25>r33s22u22v11x11z00<25\
zn0zp0zr0<2>zx0zz0zz1<24>zznzzpzzr<2>zzxzzzzzz<56>zY6zX5zX4zW3zW2<28>z5\ 0z40z30z20z10<5>w00v00u00t00t00<16>h00 }
BH_CubicManU_2 {;Union set of Critical Points, central area ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManU passes=t corners=-2.387774/2.387774/-1.790831/1.790831 params=0/0/-1.6/0/16/0 float=y maxiter=1024 inside=0 periodicity=0 colors=000g00<3>d00c00c00<24>JDDIDDHEEGEEFFFFFFFFF<24>p33r33s22<2>x11z00\ z10<24>zn0zp0zr0<2>zx0zz0zz1<24>zznzzpzzr<2>zzxzzzzzz<57>zX5zX4zW3zW2zV1\ <27>z50z40z30z20z10z00<25>h00 } BH_CubicManU_3 {;Union set of Critical Points, central area ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManU passes=t corners=-7.298743/7.298743/0.7195197/-0.7195197/-1.352909/-7.208259 params=0/0/0/1.148/16/0 float=y maxiter=8192 inside=0 logmap=73 periodicity=0 colors=000g00<3>d00c00c00<24>JDDIDDHEEGEEFFFFFFFFF<24>p33r33s22<2>x11z00\ z10<24>zn0zp0zr0<2>zx0zz0zz1<24>zznzzpzzr<2>zzxzzzzzz<57>zX5zX4zW3zW2zV1\ <27>z50z40z30z20z10z00<25>h00 } BH_CubicManLU_1 {;Lambda plane, Union set of Critical Points ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManLU passes=t corners=-2.117066/5.384655/-2.813145/2.813145 params=0/0/4/0/16/0 float=y maxiter=512 inside=0 periodicity=0 colors=@volcano.map } BH_CubicManLU_2 {;Lambda plane, Union set of Critical Points ; reset=2003 type=formula formulafile=archiv.frm formulaname=BuffHenriksenManLU passes=t corners=-2.607121/3.994351/-2.120152/2.830952 params=0/0/2/1/16/0 float=y maxiter=512 inside=0 periodicity=0 colors=@volcano.map } frm:BuffHenriksenJul {;by Xavier Buff and ;Christian Henriksen, "Julia sets in parameter spaces" ;Function: z^3 + b*z^2 + Lambda*z ;------------ ;p1 : b ;p2 : Lambda ;p3r: Bailout ;------------ ; z = pixel: z = ((z+p1)*z+p2)*z p3 >= |z| } frm:BuffHenriksenManL {;by Xavier Buff and ;Christian Henriksen, "Julia sets in parameter spaces" ;Function: z^3 + b*z^2 + lambda*z, b fixed ;periodicity=no ;------------------------------------------------------------------------- ;p1 : Perturb z(0) ;p2 : b ;p3r: Bailout ;p3i: Orbittracking(0|1) - maps either first or second Critical Point to z ;------------------------------------------------------------------------- ; zz = sqrt(sqr(p2)-3*pixel) IF (imag(p3)) z = p1 - (p2-zz)/3 zz = p1 - (p2+zz)/3 ELSE z = p1 - (p2+zz)/3 zz = p1 - (p2-zz)/3 ENDIF: z = ((z+p2)*z+pixel)*z zz = ((zz+p2)*zz+pixel)*zz p3 >= |z| && p3 >= |zz| } frm:BuffHenriksenManU {;by Xavier Buff and ;Christian Henriksen, "Julia sets in parameter space" ;Function: z^3 + b*z^2 + Lambda*z, b fixed ;U = Union of both Critical Points ;periodicity=no ;------------------------------------------------------------------------- ;p1 : Perturb z(0) ;p2 : Lambda ;p3r: Bailout ;p3i: Orbittracking(0|1) - maps either first or second Critical Point to z ;------------------------------------------------------------------------- ; zz = sqrt(sqr(pixel)-3*p2) IF (imag(p3)) z = p1 - (pixel-zz)/3 zz = p1 - (pixel+zz)/3 ELSE z = p1 - (pixel+zz)/3 zz = p1 - (pixel-zz)/3 ENDIF loop1 = loop2 = 1: IF (loop1) z = ((z+pixel)*z+p2)*z IF (p3 < |z|) loop1 = 0 ENDIF ENDIF IF (loop2) zz = ((zz+pixel)*zz+p2)*zz IF (p3 < |zz|) loop2 = 0 ENDIF ENDIF loop1 || loop2 } frm:BuffHenriksenManLU {;by Xavier Buff and ;Christian Henriksen, "Julia sets in parameter spaces" ;Function: z^3 + b*z^2 + Lambda*z, b fixed ;U = Union of both Critical Points ;periodicity=no ;------------------------------------------------------------------------- ;p1 : Perturb z(0) ;p2 : b ;p3r: Bailout ;p3i: Orbittracking(0|1) - maps either first or second Critical Point to z ;------------------------------------------------------------------------- ; zz = sqrt(sqr(p2)-3*pixel) IF (imag(p3)) z = p1 - (p2-zz)/3 zz = p1 - (p2+zz)/3 ELSE z = p1 - (p2+zz)/3 zz = p1 - (p2-zz)/3 ENDIF loop1 = loop2 = 1: IF (loop1) z = ((z+p2)*z+pixel)*z IF (p3 < |z|) loop1 = 0 ENDIF ENDIF IF (loop2) zz = ((zz+p2)*zz+pixel)*zz IF (p3 < |zz|) loop2 = 0 ENDIF ENDIF loop1 || loop2 } ------------------------- End of parameters/formulas ---------------------------