File:Critical Orbit for Golden Mean Quadratic Julia set.svg
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[edit]DescriptionCritical Orbit for Golden Mean Quadratic Julia set.svg |
English: Critical Orbit, Inner and outer circle for Golden Mean Quadratic Julia set |
Date | |
Source | Own work |
Author | Adam majewski |
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
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See also
[edit]-
Critical Orbit, Inner and outer circle of Julia set for fc(z)=z*z+c where rotation number has continued fraction expansion [0;3,2,1000,1...]
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Critical orbit tends to period 3 orbit
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3D view of critical orbit tending to parabolic fixed point
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distance between points of critical orbit in case of attracting fixed point
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parabolic case
Maxima CAS src code
[edit]kill(all) $ f(z,c):=z*z+c $ critical_orbit(c,iMax):= block( /* iMax : Number of iterations , for most cases iMax:100 */ ER:2.0, z:0+0*%i, /* first point = critical point */ orbit:[z], /* compute forward orbit */ i:0, if (abs(z)>ER) then return(orbit), loop, z:rectform(f(z,c)), orbit:endcons(z,orbit), i:i+1, if ((abs(z)<ER) and (i<iMax)) then go(loop), return(orbit) )$ /* find fixed point alfa */ GiveFixed(c):= float(rectform((1-sqrt(1-4*c))/2))$ GiveDistanceFromCenter(z):= abs(z-zf)$ GiveInnerRadiusOfOrbit(orbit):=lmin(map(GiveDistanceFromCenter,orbit))$ GiveOuterRadiusOfOrbit(orbit):=lmax(map(GiveDistanceFromCenter,orbit))$ /* =========== main =========*/ c:-.5867879078859505*%i-.3905408691260131; /* Golden Mean*/ zf:GiveFixed(c); zfx:realpart(zf)$ zfy:imagpart(zf)$ iXMax:200; NrPoints:10*iXMax; orbit:critical_orbit(c,NrPoints)$ innerRadius: GiveInnerRadiusOfOrbit(orbit) ; ir2 : innerRadius * innerRadius $ outerRadius: GiveOuterRadiusOfOrbit(orbit) ; or2 : outerRadius * outerRadius $ load(draw); draw2d( title= concat("Critical orbit, inner and outer circle for fc(z)=z*z", string(c)), user_preamble = "set size ratio 1; set key outside right; set key box ", /* */ file_name = "croGM2d", terminal = png, yrange = [-0.8,0.2], xrange = [-0.8,0.2], dimensions = [800,800], xlabel = "Z.re ", ylabel = "Z.im", point_type = filled_circle, points_joined = false, color =blue, point_size = 0.9, key = "center ", points([[realpart(zf),imagpart(zf)]]), key = "critical orbit", color =red, point_size = 0.5, points(map(realpart,orbit),map(imagpart,orbit)), ip_grid = [400,400], /* Number of initial grid points in implicit plots */ key = "inner circle", color = green, implicit( (x-zfx)^2+(y-zfy)^2 = ir2 , x,-2,2,y,-2,2), key = "outer circle", color = black, implicit( (x-zfx)^2+(y-zfy)^2 = or2 , x,-2,2,y,-2,2), color = magenta , point_size = 0.9, key = "crital point ", points([[0,0]]) );
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current | 15:59, 20 November 2011 | 800 × 800 (263 KB) | Soul windsurfer (talk | contribs) |
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Image title | Produced by GNUPLOT 4.2 patchlevel 6 |
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