File:Critical curves of real quadratic map.svg
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[edit]DescriptionCritical curves of real quadratic map.svg |
English: Critical curves of real quadratic map for periods 1,2,4,8,16 and 32 |
Date | |
Source | Own work |
Author | Adam majewski |
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Summary
[edit]Critical polynomial
[edit]
so
These polynomials are used for finding :
- centers of period n Mandelbrot set components. Centers are roots of n-th critical polynomials ( points where critical curve Qn croses x axis )
- Misiurewicz points
Maxima CAS src code
[edit]kill(all); remvalue(all); /* ---------- functions ---------------------- */ /* http://en.wikipedia.org/wiki/Complex_quadratic_polynomial */ f(z,c):=z*z+c; fn(p, z, c) := if p=0 then z elseif p=1 then f(z,c) else f(fn(p-1, z, c),c); GiveDrawList(Period,cMin, cMax, cStep):= block ( [MyList:[]], for c:cMin while c <= cMax step cStep do MyList:cons([c,fn(Period,0,c)],MyList), return(MyList) )$ compile(all); /* ---------- constant ---------------------------*/ nMax:5$ cMin:-2; cMax:0.25; cStep:0.003; /* ------------- main -----------------------*/ ColorList:[red,blue,green, black, purple , brown, cyan, violet,gray ]$ DrawLists:[]$ /* empty list */ for n:0 thru nMax do ( Period : 2^n, DrawList:GiveDrawList( Period,cMin, cMax, cStep), DrawLists:cons(points(DrawList),DrawLists), DrawLists:cons(key =concat("period =", string(Period)),DrawLists), DrawLists:cons(color=ColorList[n+1],DrawLists) ); /* ----------------- draw ------------ */ path:"~/maxima/batch/skeleton/even/test/"$ /* result of pwd; to save image in the same directory as mac file */ FileName:string(nMax)$ /* without extension which is the terminal name */ load(draw); draw2d( terminal = svg, file_name = concat(path,FileName), title = "Critical curves diagram for real quadratic map fc(z) = z^2 + c", dimensions=[2000,2000], user_preamble = "", xlabel = "c", ylabel = "z", xaxis = true, points_joined =true, point_size = 0.2, point_type = filled_circle, DrawLists );
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current | 15:51, 26 February 2014 | 2,000 × 2,000 (528 KB) | Soul windsurfer (talk | contribs) | 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 | 2000 |