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Description
((z^n+c)^2.5)/(z-c)

FractView for Android

{"source":["// Slight variation of Default, simply added branch_avg in break condition.","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;","","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","}","","func get_color(c, value) { "," var branch_avg real \u003d 0; // sum of addends",""," func breakcondition(i, znext, z, zlast, c, p, color) {"," extern addend_start int \u003d 2;"," extern addend expr \u003d \"0.5 + 0.5 sin(6 arc znext)\";",""," func bailoutcolor() {"," extern bailout real \u003d 512;"," extern max_power real \u003d 2;"," var smooth_i \u003d smoothen(znext, bailout, max_power) ;"," "," // and also add addend according to smooth_i value"," branch_avg \u003d (branch_avg + smooth_i addend) / "," (i + smooth_i - addend_start);"," "," // the next ones are only used in 3d-fractals"," extern bailoutvalue expr \u003d \"branch_avg\";"," value \u003d bailoutvalue;",""," extern bailouttransfer expr \u003d"," \"value : log(i + smooth_i)\";"," "," extern bailoutpalette palette \u003d ["," [#f80 , #f22 , #40f , #008, #080, #ff8 ],"," [#fff , #000, #fff , #000, #fff , #000]];","",""," color \u003d bailoutpalette bailouttransfer"," }"," "," func lakecolor() {"," extern epsilon real \u003d 1e-9;"," "," extern lakevalue expr \u003d \"0\";"," value \u003d lakevalue;"," "," extern laketransfer expr \u003d \"value\";"," extern lakepalette palette \u003d [[#000]];"," color \u003d lakepalette laketransfer"," }",""," { lakecolor() ; true } if not next(i, maxdepth) else // i \u003c maxdepth? then lake."," true if radrange(znext, z, bailout, epsilon, bailoutcolor(), lakecolor()) else // bailout or epsilon? "," { branch_avg \u003d branch_avg + addend ; false } if i \u003e\u003d addend_start else // do some work here"," false"," }",""," // draw single pixel"," 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 drawing procedure","do_pixel(x, y)"],"arguments":{"bools":{"light":true},"exprs":{"function":"((z^i+p)^2.5)/(z-p)","addend":"arcnorm((znext - z) / (z - zlast))"},"palettes":{"bailoutpalette":{"width":6,"height":2,"colors":[-9192984,-13972318,-832766,-10218205,-136225,-9998,-1,-16777216,-1,-16777216,-1,-16777216]}},"scales":{"Scale":[2.619681513839562E-6,7.405634420657616E-5,-7.405634420657616E-5,2.619681513839562E-6,-0.7145639228184127,-0.04839408140301874]}}}

Description
((z^n+c)^2.5)/(z-c)

FractView for Android

{"source":["// Slight variation of Default, simply added branch_avg in break condition.","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;","","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","}","","func get_color(c, value) { "," var branch_avg real \u003d 0; // sum of addends",""," func breakcondition(i, znext, z, zlast, c, p, color) {"," extern addend_start int \u003d 2;"," extern addend expr \u003d \"0.5 + 0.5 sin(6 arc znext)\";",""," func bailoutcolor() {"," extern bailout real \u003d 512;"," extern max_power real \u003d 2;"," var smooth_i \u003d smoothen(znext, bailout, max_power) ;"," "," // and also add addend according to smooth_i value"," branch_avg \u003d (branch_avg + smooth_i addend) / "," (i + smooth_i - addend_start);"," "," // the next ones are only used in 3d-fractals"," extern bailoutvalue expr \u003d \"branch_avg\";"," value \u003d bailoutvalue;",""," extern bailouttransfer expr \u003d"," \"value : log(i + smooth_i)\";"," "," extern bailoutpalette palette \u003d ["," [#f80 , #f22 , #40f , #008, #080, #ff8 ],"," [#fff , #000, #fff , #000, #fff , #000]];","",""," color \u003d bailoutpalette bailouttransfer"," }"," "," func lakecolor() {"," extern epsilon real \u003d 1e-9;"," "," extern lakevalue expr \u003d \"0\";"," value \u003d lakevalue;"," "," extern laketransfer expr \u003d \"value\";"," extern lakepalette palette \u003d [[#000]];"," color \u003d lakepalette laketransfer"," }",""," { lakecolor() ; true } if not next(i, maxdepth) else // i \u003c maxdepth? then lake."," true if radrange(znext, z, bailout, epsilon, bailoutcolor(), lakecolor()) else // bailout or epsilon? "," { branch_avg \u003d branch_avg + addend ; false } if i \u003e\u003d addend_start else // do some work here"," false"," }",""," // draw single pixel"," 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 drawing procedure","do_pixel(x, y)"],"arguments":{"bools":{"light":true},"exprs":{"function":"((z^i+p)^2.5)/(z-p)","addend":"arcnorm((znext - z) / (z - zlast))"},"palettes":{"bailoutpalette":{"width":6,"height":2,"colors":[-9192984,-13972318,-832766,-10218205,-136225,-9998,-1,-16777216,-1,-16777216,-1,-16777216]}},"scales":{"Scale":[2.619681513839562E-6,7.405634420657616E-5,-7.405634420657616E-5,2.619681513839562E-6,-0.7145639228184127,-0.04839408140301874]}}}