File:Jungreis.svg
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Summary
DescriptionJungreis.svg |
English: Boundary of Mandelbrot set as an image of unit circle under Jungreis function Polski: Brzeg Zbioru Mandelbrota jako obraz koła jednostkowego po zastosowaniu funkcji Jungreisa |
Date | |
Source | Own work : translation of maple code by G. A. Edgar; Help : G. A. Edgar and Richard J. Fateman, Robert P. Munafo and Richard J. Fateman.[1] See also : Bifurcation of Dynamic Rays in Complex Polynomials of Degree Two, Atela, P., Ergod Th & Dynam Sys (1991) 12, 401-423 |
Author | Adam majewski |
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Maxima CAS src code
/* batch file for maxima uses : - symmetry around horizontal ( 0X ) axis - Psi_M function to map conjugate plane to parameter plane - jungreis algorithm to time : 263 sec for jMax:100; and iMax:800; 4000 sec for jMax:400 */ kill(all); remvalue(all); /* ============== functions ============================================================================*/ /* ------------ computes b coefficient of Jungreis function ----*/ betaF[n,m]:=block ( [nnn:2^(n+1)-1], if m=0 then 1.0 else if ((n>0) and (m < nnn)) then 0.0 else (betaF[n+1,m]- sum(betaF[n,k]*betaF[n,m-k],k,nnn,m-nnn)-betaF[0,m-nnn])/2.0 )$ b[m]:=betaF[0,m+1]$ /* -------------------------------*/ /* Power of w to j */ wn[w,j]:= if j=0 then 1 else w*wn[w,j-1]$ /* ---------Jungreis function ; c = Psi_M(w) ----------------------------- */ Psi_M(w):=w + sum(b[j]/wn[w,j],j,0,jMax)$ /* exponential for of complex number with angle in turns */ GiveCirclePoint(t):=R*%e^(%i*t*2*%pi)$ /* gives point of unit circle for angle t in turns */ compile(all); start:elapsed_run_time (); jMax:1000; /* precision = proportional to details and time of computations */ iMax:2000; /* number of points to draw */ /* --- w-plane -----------------------------------------*/ /*-------------- unit circle ------------*/ R:1; circle_angles:makelist(i/iMax,i,0,iMax/2)$ CirclePoints:map(GiveCirclePoint,circle_angles)$ /* -------------------------parameter plane = c plane -----------------------------------*/ MPoints:map(Psi_M,CirclePoints)$ /* Mandelbrot set points */ /* add points below horizontal axis */ for w in CirclePoints do CirclePoints:cons(conjugate(w),CirclePoints)$ for c in MPoints do MPoints:cons(conjugate(c),MPoints)$ /* time */ stop:elapsed_run_time (); time:fix(stop-start); /* ---------------- draw *--------------------------------------------------------------------------*/ path : ""; /* pwd ; if you put here working directory name then graphic file will be saved in that dir */ FileName:concat(string(jMax),"jung", string(iMax))$ /* without extension which is the terminal name */ load(draw); /* Mario Rodríguez Riotorto http://www.telefonica.net/web2/biomates/maxima/gpdraw/index.html */ draw(file_name = concat(path,FileName), dimensions=[2000, 1000], terminal = 'svg, columns = 2, gr2d(title = " unit circle {w:abs(w)=1} ", point_type = filled_circle, points_joined =true, point_size = 0.34, color = red, points(map(realpart, CirclePoints),map(imagpart, CirclePoints)) ), gr2d(title = " Image of circle under Psi_M(w) ", points_joined =true, point_type = filled_circle, point_size =0.34, color = blue, points(map(realpart, MPoints),map(imagpart, MPoints)) ) );
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22 September 2014
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 16:09, 22 September 2014 | 2,000 × 1,000 (236 KB) | Soul windsurfer | User created page with UploadWizard |
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Short title | Gnuplot |
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Image title | Produced by GNUPLOT 4.6 patchlevel 4 |
Width | 2000 |
Height | 1000 |
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