File:Bifurcation diagram of complex quadratic map.png

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Bifurcation_diagram_of_complex_quadratic_map.png (640 × 480 pixels, file size: 9 KB, MIME type: image/png)

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Summary

Description
English: Bifurcation diagram of complex quadratic map.

Horizontal axis ( real slice of Mandelbrot set ) is divided int 3 segments with nonlinear scale:

  • periodic part with period doubling cascade
    • is period 1 part.
    • is rest of periodic part
  • point is the Myrberg-Feigenbaum point
  • is a chaotic part, main antenna, the shrub of family

Colors:

  • red and blue show repelling (unstable) period 1 and 2 orbits
  • green show attracting orbits

Each window has non-linear, i.e. logarithmic x-axis scale: 

                case TypSkalOsiXY of

                        liniowe : begin
                                    okno.Ax:=(okno.Dxe)/(okno.dx);  { XE=Ax*x+Bx  }
                                    okno.Bx:=XEmin-(okno.Ax*Xmin);
                                    okno.KrokX:=(okno.Dx)/(okno.Dxe);

                                    okno.Ay:=(okno.Dye)/(okno.dy);
                                    okno.By:=YEmin-(okno.Ay*Ymin);
                                    okno.KrokY:=(okno.Dy)/(okno.dye);
                                  end;

                        LogRozsz: begin  { nieliniowa , tj. logarytmiczna  skala osi x }
                                    okno.LrMin:= 0;   { logarytm naturalny }
                                    okno.LrMax:=-6;
                                    okno.dLr:=okno.LrMax-okno.LrMin;

                                    okno.XlrMin:=exp(okno.LrMin);  { Xlr = exp(Lr) }
                                    okno.XlrMax:=exp(okno.LrMax);
                                    okno.dXlr:=okno.XlrMax-okno.XlrMin;

                                    okno.Ayr:=(okno.Dye)/(okno.dy); { liniowa skala osi y }
                                    okno.Byr:=YEmin-(okno.Ayr*Ymin);
                                    okno.KrokYr:=(okno.Dy)/(okno.dye);
                                  end;

                        LogZwez : begin
                                    okno.LzMin:= -6;
                                    okno.LzMax:=  0;
                                    okno.dLz:=okno.LzMax-okno.LzMin;

                                    okno.XlzMin:=exp(okno.LzMin);
                                    okno.XlzMax:=exp(okno.LzMax);
                                    okno.dXlz:=okno.XlzMax-okno.XlzMin;

                                    okno.Ayz:=(okno.Dye)/(okno.dy); { liniowa skala osi y }
                                    okno.Byz:=YEmin-(okno.Ayz*Ymin);
                                    okno.KrokYz:=(okno.Dy)/(okno.dye);
                                  end;
                end; { case  ... }


Main program: 

PROGRAM diag321;



  { program rysuje diagram bifurkacyjny y[n+1]=y[n]*y[n]+x,
  {  x: -2.0< x <-1.41 }
  {  y: -2.0< y <2.0  }
  {  nieliniowe , zmienne w 3 oknach skalowanie osi x }
  { rysuje tez punkty stale nieprzyciagajace !!!!! }



USES {moduly standardowe}
     Crt,Graph,
     {moje moduly}
     GrafM,
     OknaM,
     fractalnyM,
     BmpM;

VAR Okno1,okno2,okno3:OkiennyT;
    Bok:integer;


BEGIN
  Opengraf;
  Bok:=Round(GetMaxx/7);

  Kojarz(okno3,-0.200,0.25,-2,2,logRozsz,(6*bok)+2,(7*bok),0,GetMaxY);
  Diagram(okno3,50,10); {unit FractalnyM}

  Kojarz(okno2,-1.401,-0.200,-2,2,logZwez,(3*bok)+1,(6*bok)+1,0,GetMaxY);
  Diagram(okno2,100,20);

  Kojarz(okno1,-2.000,-1.401,-2,2,logRozsz,0,3*bok,0,getMaxY);
  Diagram(okno1,100,200);


  ScreenCopy('b',640,480);
  Repeat until KeyPressed;
  CloseGraph;

END.
Date
Source Own work
Author Soul windsurfer
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Captions

Bifurcation diagram of complex quadratic map

Items portrayed in this file

depicts

bifurcation diagram

inception

18 November 2022

media type

image/png

checksum

c9f121466739de8672972b67751538abb57fa9ad

determination method or standard: SHA-1

data size

9,157 byte

height

480 pixel

width

640 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current15:14, 3 August 2023Thumbnail for version as of 15:14, 3 August 2023640 × 480 (9 KB)wikimediacommons>Obscure2020Optimized with OxiPNG and ZopfliPNG.
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