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Description
((z^n+c)^2)/(z-c)

FractView for Android

{"source":["// Two folds","var x int, y int, color int;","","","extern maxdepth int \u003d 120;","","// some further arguments","extern juliaset bool \u003d false;","extern juliapoint cplx \u003d -0.8:0.16;","","// c: coordinates, breakcondition: a function whether we should stop,","// value: a real variable to return some kind of value","// used in 3d-types for the height.","// returns a quat representing the color","func escapetime(c, breakcondition) {"," var i int \u003d 0,"," p cplx \u003d juliapoint if juliaset else c,"," zlast cplx \u003d 0,"," z cplx,"," znext cplx \u003d 0;",""," extern mandelinit expr \u003d \"0\";",""," z \u003d c if juliaset else mandelinit;",""," extern function expr \u003d \"mandelbrot(z, p)\";",""," var color quat;",""," while {"," znext \u003d function;"," not breakcondition(i, znext, z, zlast, c, p, color)"," } do {"," // advance to next values"," zlast \u003d z;"," z \u003d znext;"," }",""," // return color"," color","}","","// everything that is drawn must have a get_color-function.","","// c \u003d coordinates (scaled)","// value is a real variable for z-information in 3D","// but also otherwise convenient to separate drawing","// algorithm from transfer","// returns color.","func get_color(c, value) {",""," // if the fractal accumulates some values"," // like in traps or addends, here is a got place to do it."," extern foldinit expr \u003d \"0\";"," var foldvalue cplx \u003d foldinit;",""," extern foldinit2 expr \u003d \"0\";"," var foldvalue2 cplx \u003d foldinit;",""," func breakcondition(i, znext, z, zlast, c, p, color) {"," extern foldfn expr \u003d \"/cosh rad znext + foldvalue\";"," extern foldfn2 expr \u003d \"/cosh(/dist(znext, z)) + foldvalue2\";",""," func bailoutcolor() {"," extern bailout real \u003d 65536;"," extern max_power real \u003d 2;",""," // the next ones are only used in 3d-fractals"," extern bailoutvalue expr \u003d \"log(1 + foldvalue.x)\";"," value \u003d bailoutvalue ;",""," extern bailouttransfer expr \u003d \"value\";",""," extern bailoutpalette palette \u003d ["," [#a8f , #404, #fa4 , #ff8 , #f40 , #008]];",""," color \u003d bailoutpalette bailouttransfer"," }",""," func lakecolor() {"," extern epsilon real \u003d 1e-9;",""," // the next ones are only used in 3d-fractals"," extern lakevalue expr \u003d \"log(1 + foldvalue2.x)\";"," value \u003d lakevalue;",""," extern laketransfer expr \u003d"," \"arcnorm znext : value\";",""," extern lakepalette palette \u003d ["," [#fff , #fff , #fff , #fff , #fff , #fff ],"," [#a8f , #404, #fa4 , #ff8 , #f40 , #008],"," [#caf , #a4a , #fc8 , #ffc , #f82 , #24a ],"," [#000, #000, #000, #000, #000, #000]];",""," color \u003d lakepalette laketransfer"," }",""," { lakecolor() ; true } if not next(i, maxdepth) else"," true if radrange(znext, z, bailout, epsilon, bailoutcolor(), lakecolor()) else"," { foldvalue \u003d foldfn; foldvalue2 \u003d foldfn2; false }"," }",""," escapetime(c, breakcondition)","}","","","// ******************************************","// * Next are just drawing procedures. They *","// * should be the same for all drawings. *","// ******************************************","","extern supersampling bool \u003d false;","extern light bool \u003d false;","","// drawpixel for 2D","func drawpixel_2d(x, y) {"," var c cplx \u003d map(x, y);"," var value real;"," get_color(c, value) // value is not used","}","","// drawpixel for 3D","func drawpixel_3d(x, y) {"," var c00 cplx \u003d map(x, y),"," c10 cplx \u003d map(x + 1, y + 0.5),"," c01 cplx \u003d map(x + 0.5, y + 1);",""," var h00 real, h10 real, h01 real; // heights",""," // color is already kinda super-sampled"," var color \u003d (get_color(c00, h00) + get_color(c10, h10) + get_color(c01, h01)) / 3;",""," // get height out of value"," func height(value) {"," extern valuetransfer expr \u003d \"value\";"," valuetransfer"," }",""," h00 \u003d height h00; h01 \u003d height h01; h10 \u003d height h10;",""," // get the normal vector (cross product)"," var xp \u003d c10 - c00, xz \u003d h10 - h00;"," var yp \u003d c01 - c00, yz \u003d h01 - h00;",""," var np cplx \u003d (xp.y yz - xz yp.y) : (xz yp.x - xp.x yz);"," var nz real \u003d xp.x yp.y - xp.y yp.x;",""," // normalize np and nz"," var nlen \u003d sqrt(rad2 np + sqr nz);"," np \u003d np / nlen; nz \u003d nz / nlen;",""," // get light direction"," extern lightvector cplx \u003d -0.667 : -0.667; // direction from which the light is coming"," def lz \u003d sqrt(1 - sqr re lightvector - sqr im lightvector); // this is inlined",""," // Lambert\u0027s law."," var cos_a real \u003d dot(lightvector, np) + lz nz;",""," // diffuse reflexion with ambient factor"," extern lightintensity real \u003d 1;"," extern ambientlight real \u003d 0.5;",""," // if lumen is negative it is behind,"," // but I tweak it a bit for the sake of the looks:"," // cos_a \u003d -1 (which is super-behind) \u003d\u003d\u003e 0"," // cos_a \u003d 0 \u003d\u003d\u003e ambientlight"," // cos_a \u003d 1 \u003d\u003d\u003e lightintensity",""," // for a mathematically correct look use the following:"," // if cos_a \u003c 0 then cos_a \u003d 0;"," // color.a \u003d color.a * (ambientlight + lightintensity lumen);",""," def d \u003d lightintensity / 2; // will be inlined later",""," // Change L in Lab-Color"," color.a \u003d color.a (((d - ambientlight) cos_a + d) cos_a + ambientlight);",""," // Next, specular reflection. Viewer is always assumed to be in direction (0,0,1)"," extern specularintensity real \u003d 1;",""," extern shininess real \u003d 8;",""," // r \u003d 2 n l - l; v \u003d 0:0:1"," var spec_refl \u003d 2 cos_a nz - lz;",""," // 100 because L in the Lab-Model is between 0 and 100"," if spec_refl \u003e 0 then"," color.a \u003d color.a + 100 * specularintensity * spec_refl ^ shininess;",""," color","}","","func do_pixel(x, y) {"," // two or three dimensions?"," def drawpixel \u003d drawpixel_3d if light else drawpixel_2d;",""," func drawaapixel(x, y) {"," 0.25 ("," drawpixel(x - 0.375, y - 0.125) +"," drawpixel(x + 0.125, y - 0.375) +"," drawpixel(x + 0.375, y + 0.125) +"," drawpixel(x - 0.125, y + 0.375)"," );"," }",""," // which function to apply?"," def fn \u003d drawpixel if not supersampling else drawaapixel;",""," color \u003d lab2int fn(x, y)","}","","// and finally call the draing procedure","do_pixel(x, y)"],"arguments":{"ints":{"maxdepth":1200},"exprs":{"lakevalue":"log(1 + foldvalue2.x)","foldfn":"(0.5 + 0.5 cos 6 arc znext) / (12 + rad znext) + foldvalue","bailoutvalue":"log(1 + foldvalue.x)","function":"((z^i+p)^2)/(z-p)","foldfn2":"(0.5 + 0.5 cos 6 arc(z - znext)) / (12 + /dist(znext, z)) + foldvalue2"},"palettes":{"bailoutpalette":{"width":5,"height":1,"colors":[-16777114,-14522676,-14426662,-16777216,-16722167]},"lakepalette":{"width":6,"height":1,"colors":[-16777216,-5832524,-11009836,-13910531,-5912577,-1]}},"scales":{"Scale":[-1.4352260493228208E-6,0.004481024247622264,-0.004481024247622264,-1.4352260493228208E-6,-1.0022132665333232,-1.4705698832899225E-6]}}}

Description
((z^n+c)^2)/(z-c)

FractView for Android

{"source":["// Two folds","var x int, y int, color int;","","","extern maxdepth int \u003d 120;","","// some further arguments","extern juliaset bool \u003d false;","extern juliapoint cplx \u003d -0.8:0.16;","","// c: coordinates, breakcondition: a function whether we should stop,","// value: a real variable to return some kind of value","// used in 3d-types for the height.","// returns a quat representing the color","func escapetime(c, breakcondition) {"," var i int \u003d 0,"," p cplx \u003d juliapoint if juliaset else c,"," zlast cplx \u003d 0,"," z cplx,"," znext cplx \u003d 0;",""," extern mandelinit expr \u003d \"0\";",""," z \u003d c if juliaset else mandelinit;",""," extern function expr \u003d \"mandelbrot(z, p)\";",""," var color quat;",""," while {"," znext \u003d function;"," not breakcondition(i, znext, z, zlast, c, p, color)"," } do {"," // advance to next values"," zlast \u003d z;"," z \u003d znext;"," }",""," // return color"," color","}","","// everything that is drawn must have a get_color-function.","","// c \u003d coordinates (scaled)","// value is a real variable for z-information in 3D","// but also otherwise convenient to separate drawing","// algorithm from transfer","// returns color.","func get_color(c, value) {",""," // if the fractal accumulates some values"," // like in traps or addends, here is a got place to do it."," extern foldinit expr \u003d \"0\";"," var foldvalue cplx \u003d foldinit;",""," extern foldinit2 expr \u003d \"0\";"," var foldvalue2 cplx \u003d foldinit;",""," func breakcondition(i, znext, z, zlast, c, p, color) {"," extern foldfn expr \u003d \"/cosh rad znext + foldvalue\";"," extern foldfn2 expr \u003d \"/cosh(/dist(znext, z)) + foldvalue2\";",""," func bailoutcolor() {"," extern bailout real \u003d 65536;"," extern max_power real \u003d 2;",""," // the next ones are only used in 3d-fractals"," extern bailoutvalue expr \u003d \"log(1 + foldvalue.x)\";"," value \u003d bailoutvalue ;",""," extern bailouttransfer expr \u003d \"value\";",""," extern bailoutpalette palette \u003d ["," [#a8f , #404, #fa4 , #ff8 , #f40 , #008]];",""," color \u003d bailoutpalette bailouttransfer"," }",""," func lakecolor() {"," extern epsilon real \u003d 1e-9;",""," // the next ones are only used in 3d-fractals"," extern lakevalue expr \u003d \"log(1 + foldvalue2.x)\";"," value \u003d lakevalue;",""," extern laketransfer expr \u003d"," \"arcnorm znext : value\";",""," extern lakepalette palette \u003d ["," [#fff , #fff , #fff , #fff , #fff , #fff ],"," [#a8f , #404, #fa4 , #ff8 , #f40 , #008],"," [#caf , #a4a , #fc8 , #ffc , #f82 , #24a ],"," [#000, #000, #000, #000, #000, #000]];",""," color \u003d lakepalette laketransfer"," }",""," { lakecolor() ; true } if not next(i, maxdepth) else"," true if radrange(znext, z, bailout, epsilon, bailoutcolor(), lakecolor()) else"," { foldvalue \u003d foldfn; foldvalue2 \u003d foldfn2; false }"," }",""," escapetime(c, breakcondition)","}","","","// ******************************************","// * Next are just drawing procedures. They *","// * should be the same for all drawings. *","// ******************************************","","extern supersampling bool \u003d false;","extern light bool \u003d false;","","// drawpixel for 2D","func drawpixel_2d(x, y) {"," var c cplx \u003d map(x, y);"," var value real;"," get_color(c, value) // value is not used","}","","// drawpixel for 3D","func drawpixel_3d(x, y) {"," var c00 cplx \u003d map(x, y),"," c10 cplx \u003d map(x + 1, y + 0.5),"," c01 cplx \u003d map(x + 0.5, y + 1);",""," var h00 real, h10 real, h01 real; // heights",""," // color is already kinda super-sampled"," var color \u003d (get_color(c00, h00) + get_color(c10, h10) + get_color(c01, h01)) / 3;",""," // get height out of value"," func height(value) {"," extern valuetransfer expr \u003d \"value\";"," valuetransfer"," }",""," h00 \u003d height h00; h01 \u003d height h01; h10 \u003d height h10;",""," // get the normal vector (cross product)"," var xp \u003d c10 - c00, xz \u003d h10 - h00;"," var yp \u003d c01 - c00, yz \u003d h01 - h00;",""," var np cplx \u003d (xp.y yz - xz yp.y) : (xz yp.x - xp.x yz);"," var nz real \u003d xp.x yp.y - xp.y yp.x;",""," // normalize np and nz"," var nlen \u003d sqrt(rad2 np + sqr nz);"," np \u003d np / nlen; nz \u003d nz / nlen;",""," // get light direction"," extern lightvector cplx \u003d -0.667 : -0.667; // direction from which the light is coming"," def lz \u003d sqrt(1 - sqr re lightvector - sqr im lightvector); // this is inlined",""," // Lambert\u0027s law."," var cos_a real \u003d dot(lightvector, np) + lz nz;",""," // diffuse reflexion with ambient factor"," extern lightintensity real \u003d 1;"," extern ambientlight real \u003d 0.5;",""," // if lumen is negative it is behind,"," // but I tweak it a bit for the sake of the looks:"," // cos_a \u003d -1 (which is super-behind) \u003d\u003d\u003e 0"," // cos_a \u003d 0 \u003d\u003d\u003e ambientlight"," // cos_a \u003d 1 \u003d\u003d\u003e lightintensity",""," // for a mathematically correct look use the following:"," // if cos_a \u003c 0 then cos_a \u003d 0;"," // color.a \u003d color.a * (ambientlight + lightintensity lumen);",""," def d \u003d lightintensity / 2; // will be inlined later",""," // Change L in Lab-Color"," color.a \u003d color.a (((d - ambientlight) cos_a + d) cos_a + ambientlight);",""," // Next, specular reflection. Viewer is always assumed to be in direction (0,0,1)"," extern specularintensity real \u003d 1;",""," extern shininess real \u003d 8;",""," // r \u003d 2 n l - l; v \u003d 0:0:1"," var spec_refl \u003d 2 cos_a nz - lz;",""," // 100 because L in the Lab-Model is between 0 and 100"," if spec_refl \u003e 0 then"," color.a \u003d color.a + 100 * specularintensity * spec_refl ^ shininess;",""," color","}","","func do_pixel(x, y) {"," // two or three dimensions?"," def drawpixel \u003d drawpixel_3d if light else drawpixel_2d;",""," func drawaapixel(x, y) {"," 0.25 ("," drawpixel(x - 0.375, y - 0.125) +"," drawpixel(x + 0.125, y - 0.375) +"," drawpixel(x + 0.375, y + 0.125) +"," drawpixel(x - 0.125, y + 0.375)"," );"," }",""," // which function to apply?"," def fn \u003d drawpixel if not supersampling else drawaapixel;",""," color \u003d lab2int fn(x, y)","}","","// and finally call the draing procedure","do_pixel(x, y)"],"arguments":{"ints":{"maxdepth":1200},"exprs":{"lakevalue":"log(1 + foldvalue2.x)","foldfn":"(0.5 + 0.5 cos 6 arc znext) / (12 + rad znext) + foldvalue","bailoutvalue":"log(1 + foldvalue.x)","function":"((z^i+p)^2)/(z-p)","foldfn2":"(0.5 + 0.5 cos 6 arc(z - znext)) / (12 + /dist(znext, z)) + foldvalue2"},"palettes":{"bailoutpalette":{"width":5,"height":1,"colors":[-16777114,-14522676,-14426662,-16777216,-16722167]},"lakepalette":{"width":6,"height":1,"colors":[-16777216,-5832524,-11009836,-13910531,-5912577,-1]}},"scales":{"Scale":[-1.4352260493228208E-6,0.004481024247622264,-0.004481024247622264,-1.4352260493228208E-6,-1.0022132665333232,-1.4705698832899225E-6]}}}