File:Lyapunov exponent of real quadratic map with exponential transformation on the real axis.png
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Summary
DescriptionLyapunov exponent of real quadratic map with exponential transformation on the real axis.png |
English: Lyapunov exponent of real quadratic map with exponential transformation on the real axis |
Date | |
Source | Own work : based on the code by Mario Rodriguez Riotorto[1] using Maxima CAS and draw package ( also by Mario Rodriguez Riotorto ) |
Author | Adam majewski |
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Licensing
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Maxima CAS src code
/* batch file for Maxima CAS program save it as a file with mac extension and open in Maxima It creates l6.svg file in the directory path ( see below) change the path directory if you save mac file in the different location https://commons.wikimedia.org/wiki/File:Lyapunov_exponent_of_real_quadratic_map.png http://fy.chalmers.se/~f99krgu/CompBioA/CompBioLecture2.pdf log(c - cf) log(-c_f) = 0.3372970313844768 log(0.25-c_f) = 0.5014751574920848 --------------- Transform is c←ec+c0 with c0=−1.401155189092051. https://fractalforums.org/fractal-image-gallery/18/feigenbaum-stretch/2112 -------------- */ kill(all); remvalue(all); /* real quadratic diagram based on the code by Mario Rodriguez Riotorto using Maxima CAS draw packag */ pts:[]; /* points of the orbit */ ls:[]; kMax1:200; kMax2:500; cF:-1.4011551890; /* The Feigenbaum Point of period doubling cascade */ cMax: 0.25; xMax : log(cMax - cF); /* from c to x */ /* width of component is about 1.5 */ NoOfComponents : 8 ; /* (xMax-xMin)/1.5; */ xMin : xMax - NoOfComponents*1.5; /* from NoOfComponents to x */ cMin: cF +exp(xMin); /* from x to c = -1.3996312; */ n:500; dx:(xMax-xMin)/n; /* ------------- compute -----------------------------------*/ for x:xMin while x <= xMax step dx do ( c: cF + exp(x), z: 0.0, l:0, /* Lyapunov exponent */ for k:1 thru kMax1 do ( z: z * z+c, /* to remove points from image compute and do not draw it */ l:l+log(abs(2*z)) ), for k:1 thru kMax2 do ( z: z * z+c, /* compute and draw it */ pts: cons([x,z], pts),/* save points to draw it later */ l:l+log(abs(2*z)) ), ls:cons([x,l/(kMax1+kMax2)],ls) /* save points to draw it later */ ); /* ================= draw ======================================*/ path:"~/maxima/batch/logistic/log/m2/"$ /* result of pwd; to save image in the same directory as mac file */ FileName:concat("n_",string(NoOfComponents), "_", string(n),"_", string(kMax1),"_",string(kMax2))$ /* without extension which is the terminal name */ load(draw); draw( terminal = 'svg, file_name = concat(path,FileName), dimensions=[1900,2600], /* y = x*rows */ gr2d( title = "Bifurcation diagram, z[i+1] = z[i]*z[i] +c", font_size = 30, font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */ points_joined =false, xlabel = "log(c - cF)", ylabel = "z ", point_type = filled_circle, point_size = 0.2, color = black, points(pts) ), gr2d( title = " Lyapunov exponent ", font_size = 30, font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */ points_joined =true, yaxis = true, xaxis = true, xlabel = "log(c - cF)", ylabel = " lyapunov exponent ", yrange = [-0.5,0.1], color = red, point_size = 0.5, point_type = filled_circle, points(ls)) );
Image Mafic / Bash src code
convert n_8_500_200_500.svg n.png
Items portrayed in this file
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28 September 2019
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 05:01, 29 September 2019 | 1,799 × 2,462 (263 KB) | Soul windsurfer | User created page with UploadWizard |
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Horizontal resolution | 35.79 dpc |
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Vertical resolution | 35.79 dpc |
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