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[] https://en.wikipedia.org/wiki/Hyperoperation[] https://en.wikipedia.org/wiki/Tetration[] Galidakis,IoannisandWeisstein,EricW."PowerTower."FromMathWorldAWolframWeb Resource.http://mathworld.wolfram.com/PowerTower.html

[] Weisstein,EricW."ArrowNotation."FromMathWorldAWolframWebResource. http://mathworld.wolfram.com/ArrowNotation.html

[] Knuth,DonaldE.(1976)."MathematicsandComputerScience:CopingwithFiniteness".Science194 (4271):12351242.doi:10.1126/science.194.4271.1235.PMID17797067

[] R.L.Goodstein(Dec.1947)."TransfiniteOrdinalsinRecursiveNumberTheory".JournalofSymbolic Logic12(4):123129.doi:10.2307/2266486.JSTOR2266486

[] AlbertA.Bennett(Dec.1915)."NoteonanOperationoftheThirdGrade".AnnalsofMathematics, SecondSeries17(2):7475.doi:10.2307/2007124.JSTOR2007124

[] Weisstein,EricW."Peano'sAxioms."FromMathWorldAWolframWebResource.http://mathworld.wolfram.com/PeanosAxioms.html

[] Knoebel,R.A."ExponentialsReiterated."Amer.Math.Monthly88,235252,1981. [] Knuth.Twonotesonnotation.(AMM99no.5(May1992),403422).[] D.Kouznetsov(July2009)."Solutionof ( 1) exp( ( ))F z F z incomplex z plane". MathematicsofComputation78(267):16471670.doi:10.1090/S0025571809021887

[] Corless,R.M.;Gonnet,G.H.;Hare,D.E.G.;Jeffrey,D.J.;Knuth,D.E.(1996). "OntheLambertW function"(PostScript).AdvancesinComputationalMathematics5:333. doi:10.1007/BF02124750

[] Weisstein,EricW."Graham'sNumber."FromMathWorldAWolframWebResource. http://mathworld.wolfram.com/GrahamsNumber.html

[] Weisstein,EricW."LambertWFunction."FromMathWorldAWolframWebResource. http://mathworld.wolfram.com/LambertWFunction.html

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Z1 = -0.0817 -0.0756 i Z2 = -0.91904047 + 0.10235303999999999 i Z3 =-0.0858407592994207 -0.09813317197505758 i Z4 = -0.9222614834847852 + 0.10684765198959914 i Z5 = -0.08085017681613382 -0.10708294806158752 i Z6 = -0.9249300066743605 + 0.10731535056954444 i Z7 = -0.07602106722123159 -0.10851837583710017 i

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... Z158 = -0.10871738176813076 + 0.04678616835683036 i Z159 = -0.09036947645099619 + 0.6898270605465648 i Z160 = -0.567694731188287 + 0.5753213793933545 i Z161 = -0.10871738176813076 + 0.04678616835683036 i Z162 = -0.09036947645099619 + 0.6898270605465648 i Z163 = -0.567694731188287 + 0.5753213793933545 i

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1 2 3 4 5 6 canvas = document.getElementById("Output"); 7 context = canvas.getContext("2d"); 8 9 view = [0,0]; 10 zoom = 1; 11 iteration = 1000; 12 13 function mandelbrot(px,py) 14 { 15 Cx = (px-canvas.width/2)/(canvas.width*zoom/4) + view[0]; 16 Cy = (py-canvas.height/2)/(canvas.width*zoom/4) + view[1]; 17 x = Cx ; 18 y = Cy ; 19 20 for (n = 0; n < iteration && x*x + y*y

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1 2 3 4 5 6 canvas = document.getElementById("Output"); 7 context = canvas.getContext("2d"); 8 9 view = [0,0]; 10 zoom = 1; 11 iteration = 1000; 12 13 function mandelbrot(px,py) 14 { 15 Cx = (px-canvas.width/2)/(canvas.width*zoom/4) + view[0]; 16 Cy = (py-canvas.height/2)/(canvas.width*zoom/4) + view[1]; 17 x = Cx ; 18 y = Cy ; 19 20 for (n = 0; n < iteration && x*x + y*y 1) {s = 1} 51 if (v < 0) {v = 0} 52

if (v > 1) {v = 1} 53 if (i == 0) {R = v; G = v*(1-s+s*f); B = v*(1-s); }else 54 if (i == 1) {R = v*(1-s*f); G = v; B = v*(1-s); }else 55 if (i == 2) {R = v*(1-s); G = v; B = v*(1-s+s*f);}else 56 if (i == 3) {R = v*(1-s); G = v*(1-s*f); B = v; }else 57 if (i == 4) {R = v*(1-s+s*f); G = v*(1-s); B = v; }else 58 {R = v; G = v*(1-s); B = v*(1-s*f); } 59 60 return {r:Math.round(R*256) ,g:Math.round(G*256) ,b:Math.round(B*256)}; 61 } 62 63 function interpolation(PX,PY) 64 { 65 d = 0.25; 66 67 C1 = color(mandelbrot(PX-d,PY-d)); 68 C2 = color(mandelbrot(PX-d,PY+d)); 69 C3 = color(mandelbrot(PX+d,PY-d)); 70 C4 = color(mandelbrot(PX+d,PY+d)); 71 72 return {r: Math.round((C1.r + C2.r + C3.r + C4.r)/4), 73 g: Math.round((C1.g + C2.g + C3.g + C4.g)/4), 74 b: Math.round((C1.b + C2.b + C3.b + C4.b)/4)}; 75 } 76 77 function draw() 78 { 79 for (Px = 0; Px < canvas.width; Px += 1) 80 { 81 rgb = interpolation(Px,Py); 82 context.fillStyle = "rgb("+ rgb.r +","+ rgb.g +","+ rgb.b +")"; 83 context.fillRect(Px,Py,1,1); 84 } 85 86 Py += 1; 87 88 if(Py

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1 2 3 4 5 6 canvas = document.getElementById("Output"); 7 context = canvas.getContext("2d"); 8 9 view = [0.2523076404107750245,0.000177232451031179527]; 10 zoom = 1121184869.0216826146436341797303; 11 iteration = 5000; 12 13 function mandelbrot(px,py) 14 { 15 Cx = (px-canvas.width/2)/(canvas.width*zoom/4) + view[0]; 16 Cy = (py-canvas.height/2)/(canvas.width*zoom/4) + view[1]; 17 x = Cx; 18 y = Cy; 19 dz = [1,0]; 20 21 for (n = 0; n < iteration && x*x + y*y 1) {s = 1} 56 if (v < 0) {v = 0} 57 if (v > 1) {v = 1} 58 if (i == 0) {R = v; G = v*(1-s+s*f); B = v*(1-s); }else 59 if (i == 1) {R = v*(1-s*f); G = v; B = v*(1-s); }else 60

if (i == 2) {R = v*(1-s); G = v; B = v*(1-s+s*f);}else 61 if (i == 3) {R = v*(1-s); G = v*(1-s*f); B = v; }else 62 if (i == 4) {R = v*(1-s+s*f); G = v*(1-s); B = v; }else 63 {R = v; G = v*(1-s); B = v*(1-s*f); } 64 65 return {r:Math.round(R*256),g:Math.round(G*256),b:Math.round(B*256)}; 66 } 67 68 function interpolation(PX,PY) 69 { 70 d = 0.25; 71 72 C1 = color(mandelbrot(PX-d,PY-d)); 73 C2 = color(mandelbrot(PX-d,PY+d)); 74 C3 = color(mandelbrot(PX+d,PY-d)); 75 C4 = color(mandelbrot(PX+d,PY+d)); 76 77 return {r: Math.round((C1.r + C2.r + C3.r + C4.r)/4), 78 g: Math.round((C1.g + C2.g + C3.g + C4.g)/4), 79 b: Math.round((C1.b + C2.b + C3.b + C4.b)/4)}; 80 } 81 82 function draw() 83 { 84 for (Px = 0; Px < canvas.width; Px += 1) 85 { 86 rgb = interpolation(Px,Py); 87 context.fillStyle = "rgb("+ rgb.r +","+ rgb.g +","+ rgb.b +")"; 88 context.fillRect(Px,Py,1,1); 89 } 90 91 Py += 1; 92 93 if(Py

:

1.76857365631527099328174291532954471293412005340554988233751113528277655336463538201197793353633219864780879587457664323003444860982060845884452916908328537926083358113196132348066749594983804325362691224044888474536466283249590645430.0009642968513582800001762427203738194482747761226565635652857831533070475543666558930286153827950716700828887932578932976924523447497708248894734256480183898683164582055541842171815899305250842692638349057118793296768325124255746563i

rendering 6 teamfresh . ! 6.06610228 . .

. .

fractus.ir

: []TheBeautyofFractals:ImagesofComplexDynamicalSystems,HeinzOttoPeitgen,PeterH.Richter[]OnSmoothFractalColoringTechniques,Hrknen,Jussi[]Coloringdynamicalsystemsinthecomplexplane,FranciscoGarcia,AngelFernandez,JavierBarrallo,LuisMartin[]DeladinmicaalageometraenelconjuntodeMandelbrot,IigoQuilez[]InspectionsontheMandelbrotSetsofMonicOneDimensionalPolynomials,IigoQuilez []CanWeSeetheMandelbrotSet?,JohnEwing,TheCollegeMathematicsJournal,Vol.26,No.2(March1995)[]OperatingwithexternalargumentsintheMandelbrotsetantenna.G.Pastor,M.Romera,G.Alvarez,F.Montoya[]http://en.wikipedia.org/wiki/Mandelbrot_set[]http://mathworld.wolfram.com/MandelbrotSet.html[]http://mrob.com/pub/muency.html[]http://guciek.github.com/web_mandelbrot.html[]http://cosinekitty.com/mandel_orbits_analysis.html[]http://www.ricsfractals.net/math/banach/banach.htm[]http://www.physics.arizona.edu/~restrepo/475A/Notes/sourcea/node21.html[]http://iquilezles.org/www/articles/distancefractals/distancefractals.htm[]http://fanf.livejournal.com/110025.html[]http://hdfractals.com/lastlightson/[]http://tech-algorithm.com/articles/bilinear-image-scaling/[]http://en.wikipedia.org/wiki/HSL_and_HSV

: . FoxitReader5.3 AdobeReader10

http://tech-algorithm.com/articles/bilinear-image-scaling/http://hd-fractals.com/last-lights-on/http://fractus.ir/

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