File:Miim.jpg
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Miim.jpg (500 × 500 pixels, file size: 31 KB, MIME type: image/jpeg)
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Contents
Summary
DescriptionMiim.jpg | Julia set F(z)=z*z+c for c:-0.11+0.65569999*%i; Made with Maxima using MIIM |
Source | Own work |
Author | Adam majewski |
Info
Orbit of critical point tends to period 3 attracting cycle :
- 0.17434140717278*%i-0.23080799291989
- 0.57522120945524*%i-0.087122596659277
- 0.55547045915754*%i-0.4332890929585
Absolute value of multiplier of above cycle is 0.94840556944351
Licensing
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Maxima source code
/* this is batch file for Maxima 5.13.0 http://maxima.sourceforge.net/ tested in wxMaxima 0.7.1 using draw package ( interface to gnuplot ) to draw on the screen draws Julia set for f(z)=z*z+c using modified IIM modification: stop reversed iteration if pixel was hit in reversed orbit > HitLimit times Adam Majewski */ c:-0.11+0.65569999*%i; /* */ HitLimit:14; /* proportional to number of details and time of drawing */ /* resolution is proportional to number of details and time of drawing */ iXmax:500; iYmax:500; /* define image size : width:iXmax-0+1; heght:iYmax-0+1 ; */ start:elapsed_run_time (); NumberOfPoints:0; f(z,c):=z*z+c; finverseplus(z,c):=sqrt(z-c); finverseminus(z,c):=-sqrt(z-c); /* define z-plane ( dynamical ) */ zxMin:-2.0; zxMax:2.0; zyMin:-2.0; zyMax:2.0; /* */ PixelWidth:(zxMax-zxMin)/iXmax; PixelHeight:(zyMax-zyMin)/iYmax; array(Hits,iXmax,iYmax); /* 2D array of hits pixels . Hit > 0 means that point was in orbit */ /* no hits for beginning */ for iX:0 thru iXmax step 1 do for iY:0 thru iYmax step 1 do Hits[iX,iY]:0; /* compute fixed points of f(z,c) : z=f(z,c) */ fixed:float(rectform(solve([z*z+c=z],[z]))); /* Find which is repelling */ if (abs(2*rhs(fixed[1]))<1) then block( beta:rhs(fixed[1]), alfa:rhs(fixed[2]) ) else block( alfa:rhs(fixed[1]), beta:rhs(fixed[2]) ); /* choose repeller as a starting point */ /*save beta in stack */ stack:[beta]; /* make 2 list of points and copy beta to to lists */ xx:makelist (realpart(beta), i, 1, 1); /* list of re(z) */ yy:makelist (imagpart(beta), i, 1, 1); /* list of im(z) */ NumberOfPoints:1; /* reversed iteration of beta */ block (loop, z:last(stack), stack:delete(z,stack), /* inverse iteration - first preimage (root) */ z:finverseplus(z,c), /* translate from world to screen coordinate */ iX:fix((realpart(z)-zxMin)/PixelWidth), iY:fix((imagpart(z)-zyMin)/PixelHeight), hit:Hits[iX,iY], if hit<HitLimit then block( Hits[iX,iY]:hit+1, stack:endcons(z,stack), /* push = add z at the end of list stack */ if hit=0 then block( xx:cons(realpart(z),xx), yy:cons(imagpart(z),yy)), NumberOfPoints:NumberOfPoints+1 ), /* inverse iteration - second preimage (root) */ z:-z, /* translate from world to screen coordinate, coversion to integer */ iX:fix((realpart(z)-zxMin)/PixelWidth), iY:fix((imagpart(z)-zyMin)/PixelHeight), hit:Hits[iX,iY], if hit<HitLimit then block( Hits[iX,iY]:hit+1, /* push = add z at the end of list stack to continue iteration */ stack:endcons(z,stack), if hit=0 then block( xx:cons(realpart(z),xx), yy:cons(imagpart(z),yy)), /* draw point */ NumberOfPoints:NumberOfPoints+1 ), if is(not emptyp(stack)) then go(loop) ); stop:elapsed_run_time (); t:fix(stop-start); /* draw reversed orbit of beta using draw package */ load(draw); draw2d( file_name = "miim", terminal = 'png, pic_width = iXmax, pic_height = iYmax, yrange = [zyMin,zyMax], xrange = [zxMin,zyMax], title= "Julia set in dynamical plane for f(z,c):=z*z+c drawn using MIIM", key = concat("c=",string(c),". There are ",string(NumberOfPoints)," points" ), label ([concat("HitLimit=",string(HitLimit)," Time=",string(t)),-1.2,-1.8]), xlabel = "Z.re ", ylabel = "Z.im", point_type = dot, point_size = 8, color = black, points(xx,yy) );
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 21:01, 28 February 2008 | 500 × 500 (31 KB) | Soul windsurfer | {{Information |Description= |Source=self-made |Date= |Author= Adam majewski |Permission= |other_versions= }} |
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