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| Keywords: Demm 2000 Mandelbrot set.jpg Mandelbrot set for F z z z+c using Milnor algorithm DEM/M own Adam majewski Adam majewski Compare with <gallery> File Mandelbrot set rainbow colors png Image with C++ code without zoom and different algorithm File Mandelbrot set zoom with continous escape time png contiunous escape time with c code File Mandelbrot set 10000px png continous colour but without algorithm </gallery> The image contains a rectangular region corners of c-plane C_Plane eCxMin -2 5 C_Plane eCxMax 1 5 C_Plane eCyMin -2 C_Plane eCyMax 2 center and sides of c-plane C_Plane Center x -0 5 C_Plane Center y 0 C_Plane width 4 C_Plane height 4 Bitmap size in pixels Bitmap Width 3000 Bitmap Height 3000 Number of bitmap points 9000000 points Drawing Time 21625 miliseconds Bitmapa PixelFormat pf32bit Maximal number of iterations 1000 Escape Radius 100 Image is made with program http //fraktal republika pl/mandel html MandelbrotSetExplorer It is made using programing language object Pascal IDE Borland Delphi 6 0 - 7 0 personal edition - 10 0 Turbo Explorer programing style libaries standard VCL OS windows Bitmap image is transformed to jpg with IrfanView author Adam Majewski fraktal republika pl 20003- 2007 Delphi Pascal src code <pre> spoken language english programming language Pascal Borland object Pascal compiler VER 140 IDE Borland Delphi 7 0 personal edition programming style obiektowy programming method visual RAD target CPU library standard VCL program type GUI application licence GNU GPL OS win32 windows 98 SE hardware PC platform ix86 author Adam Majewski adammaj1- at - o2 - dot - pl republika pl/fraktal walbrzych poland 2005 12 12 </pre> Computing color from RGB gradient <source lang pascal> // function Rainbow iMin iMax i Integer TColor; // gives rainbow gradient of color // Opracował Witold J Janik; WJJ CAD PL // // Funkcja FnTecza umożliwia narysowanie // tęczy przy zmianie i od iMin do iMax // podziękowania dla Andrzeja Wšsika z pl comp lang delphi // http //4programmers net/view php id 201 var m Double; r g b mt Byte; begin m i - iMin / iMax - iMin + 1 6; mt abs round frac m FF ;// added abs ; why erange check eror case Trunc m of 0 begin R FF; G mt; B 0; end; 1 begin R FF - mt; G FF; B 0; end; 2 begin R 0; G FF; B mt; end; 3 begin R 0; G FF - mt; B FF; end; 4 begin R mt; G 0; B FF; end; 5 begin R ff; G 0; B FF - mt; end; end; // case Result rgb R G B ; end; //------------------------------- </source> exterior Distance Estimastion Method for Mandelbrot set DEM/M <source lang pascal> Function PointIsInCardioid Cx Cy extended boolean; //Hugh Allen // http //homepages borland com/ccalvert/Contest/MarchContest/Fractal/Source/HughAllen zip var DeltaX DeltaY extended; // PDeltyX PDeltyY extended; // ZFixedX ZFixedY extended; begin result false; // cardioid checkig - thx to Hugh Allen //sprawdzamy Czy punkt C jest w głównej kardioidzie //Cardioid in squere -0 75 0 4 x -0 65 0 65 if InRange Cx -0 75 0 4 and InRange Cy -0 65 065 then begin // M1 all C for which Fc z has attractive stable fixed point // znajdyjemy punkt staly z z z z+c // czyli rozwiazujemy rownanie kwadratowe // zmiennej zespolonej o wspolczynnikach zespolonych // Z Z - Z + C 0 //Delta 1-4 a c; Delta i C sa liczbami zespolonymi DeltaX 1-4 Cx; DeltaY -4 Cy; // Pierwiastek zespolony z delty CmplxSqrt DeltaX DeltaY PDeltyX PDeltyY ; // obliczmy punkt staly jeden z dwóch ten jest prawdopodobnie przycišgajšcy ZFixedX 1 0-PDeltyX; //0 5-0 5 PDeltyX; ZFixedY PDeltyY; //-0 5 PDeltyY; // jesli punkt stały jest przycišgajšcy // to należy do M1 If ZfixedX ZFixedX + ZFixedY ZFixedY <1 0 then result true; // ominięcie iteracji M1 przyspiesza 3500 do 1500 msek end; // if InRange Cx end; //------------------------------------ Function PointIsInComponent Cx Cy extended boolean; //Hugh Allen // http //homepages borland com/ccalvert/Contest/MarchContest/Fractal/Source/HughAllen zip var Dx extended; begin result false; // czy punkt C nalezy do koła na lewo od kardioidy // circle center -1 0 and radius 1/4 dx Cx+1 0; if Dx Dx+Cy Cy < 0 0625 then result true; end; Function GiveDistance xy2 eDx eDy extended extended; begin result 2 log2 sqrt xy2 sqrt xy2 /sqrt sqr eDx +sqr eDy ; end; //------------------------------------ //------------------------------ Procedure DrawDEM_DazibaoTrueColor; // draws Mandelbrot set in black and its complement in true color // see http //ibiblio org/e-notes/MSet/DEstim htm // by Evgeny Demidov // // see also //http //www mandelbrot-dazibao com/Mset/Mset htm // translation with modification of Q-Basic program // http //www mandelbrot-dazibao com/Mset/Mdb3 bas // // see also my page http //republika pl/fraktal/mset_dem html var iter integer; iY iX integer; eCy eCx extended; // C eCx + eCy i eX eY extended; // Zn eX+eY i eTempX eTempY extended; eX2 eY2 extended; //x2 eX eX; y2 eY eY; eXY2 extended; // xy2 x2+y2; eXY4 extended; eTempDx eTempDy extended; eDx eDy extended; // derivative distance extended; color TColor; begin //compute bitmap for iY iYmin to iYMax do begin eCy Convert_iY_to_eY iY ; for iX iXmin to iXmax do begin eCx Convert_iX_to_eX iX ; If not PointIsInCardioid eCx eCy and not PointIsInComponent eCx eCy then begin // Z0 0+0 i eX 0; eY 0; eTempX 0; eTempY 0; // eX2 0; eY2 0; eXY2 0; // eDx 0; eDy 0; eTempDx 0; eTempDy 0; // iter 0; // iteration of Z ; Z Z z +c while iter<IterationMax and eXY2< BailOut2 do begin inc iter ; // eTempY 2 eX eY + eCy; eTempX eX2-eY2 + eCx; // eX2 eTempX eTempX; eY2 eTempY eTempY; // eTempDx 1+2 eX eDx-eY eDy ; eTempDy 2 eX eDY+eY eDx ; // eXY2 eX2+eY2; // eX ETempX; eY eTempY; // eDx eTempDx; eDy eTempDy; end; // while // drawing procedure if iter<IterationMax then begin distance GiveDistance eXY2 eDx eDy ; color Rainbow 1 500 Abs Round 100 Log10 distance mod 500 ; with Bitmap1 FirstLineiY Bitmap1 LineLength+iX do begin B GetBValue color ; G GetGValue color ; R GetRValue color ; //A 0; end; // with FirstLineY LineLength+X end // if iter<IterationMax then else with Bitmap1 FirstLineiY Bitmap1 LineLength+iX do begin B 0; G 0; R 0; //A 0; end; //--- end of drawing procedure --- end // If not PointIsInCardioid then else with Bitmap1 FirstLineiY Bitmap1 LineLength+iX do begin B 0; G 0; R 0; //A 0; end; //--- If not PointIsInCardioid end; // for iX end; // for iY end; //------------------------------------------------------ </source> Bitmap <source lang pascal> Interface uses graphics; CONST PixelCountMax 32768; TYPE //http //www efg2 com/Lab/ImageProcessing/Scanline htm // 24-bit color bitmap TRGBTriple RECORD rgbtBlue BYTE; rgbtGreen BYTE; rgbtRed BYTE; END; TRGBTripleArray ARRAY0 PixelCountMax-1 OF TRGBTriple; pRGBTripleArray TRGBTripleArray; // TRGB32 record B G R A Byte; end; TRGB32Array array0 MaxInt div SizeOf TRGB32 -1 of TRGB32; PRGB32Array TRGB32Array; //----------------------- TBitmap32bit class TBitmap public LineLength Longint; FirstLine PRGB32Array; Procedure Default; Procedure Clear; Procedure Refresh; end; // class //-------------------------- Var Bitmap1 TBitmap32bit; iXmin iYmin iXmax iYmax integer; // pf24bit LineLength24 Longint; FirstLine24 pRGBTripleArray; Row24 pRGBTripleArray; //---------------------------------------------------- Implementation //---------------------------------------------------- Procedure TBitmap32bit Default; begin Bitmap1 Width 400; // Bitmap1 Height 400; // // Bitmap1 Refresh; end; //------------------------------------------ Procedure TBitmap32bit Clear; // clear make white all points of the Bitmap1 var iX iY integer; begin for iX 0 to Bitmap1 Width-1 do For iY 0 to Bitmap1 Height-1 do with Bitmap1 FirstLineiY Bitmap1 LineLength+iX do begin // all points white B 255; G 255; R 255; //A 0; end; end; //--------------------------------------------------------------- Procedure TBitmap32bit Refresh; begin iXmin 0; iYmin 0; iXmax Bitmap1 Width-1; iYmax Bitmap1 Height-1; // Bitmap1 FirstLine Bitmap1 Scanline0; Bitmap1 LineLength Longint Bitmap1 Scanline1 - Longint Bitmap1 FirstLine div SizeOf TRGB32 ; // end; //--------------------------------------------- Initialization Bitmap1 TBitmap32bit Create; construct the Bitmap1 object // Bitmap1 PixelFormat pf32bit; // Bitmap1 Default; // see BitmapU //--------------------------------------- END </source> Mandelbrot sets whole Images created or edited with IrfanView Images with Pascal source code | ||||
