File:DistanceToFixed.png
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Summary
DescriptionDistanceToFixed.png |
English: Distance to fixed point for various types of local discrete dynamics near fixed point . Polski: Typy lokalnej dynamiki w otoczeniu punktu stałego |
Date | |
Source | Own work |
Author | Adam majewski |
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Maxima CAS src code
/* gives distance between 2 complex points on plane */ kill(all); /* ---------- functions ---------------------- */ /* http://en.wikipedia.org/wiki/Complex_quadratic_polynomial */ f(z,c):=rectform(z*z+c); /* find fixed point alfa of function f(z,c) */ GiveFixed(c):= float(rectform((1-sqrt(1-4*c))/2))$ GivePlaneDistance(z1,z2):=float(abs(z2-z1))$ GiveList(z0,c, iMax):= block ( [i,zAlfa,zprev,znext,dist,d_list], zAlfa:GiveFixed(c), zprev:z0, znext:f(zprev,c), dist:GivePlaneDistance(zAlfa,znext), d_list:[[1,dist]], zprev : znext, i:1, while abs(znext)<2 and i<iMax do ( znext:f(zprev,c), dist:GivePlaneDistance(zAlfa,znext), d_list:endcons([i,dist],d_list), zprev : znext, i:i+1 ), return(d_list) )$ /* conformal map from circle to cardioid ( boundary of period 1 component of Mandelbrot set */ F(w):=w/2-w*w/4; /* circle D={w:abs(w)=1 } where w=l(t,r) t is angle in turns ; 1 turn = 360 degree = 2*Pi radians r is a radius */ ToCircle(t,r):=r*%e^(%i*t*2*%pi); compile(all)$ /* ---------- constant ---------------------------*/ Numerator :1; denominator :2; internalAngle: Numerator/denominator; internalRadius:1; iMax:500; zcr : 0.0; /* ------------- main -----------------------*/ /* parabolic */ w1:ToCircle(internalAngle,internalRadius); /* point of circle */ cp: float(rectform(F(w1))) ; /* point of period 1 component of Mandelbrot set */ ParabolicList:GiveList(zcr,cp,iMax); /* siegel*/ cs:-.5867879078859505*%i-.3905408691260131; z0s: 1.006250000000000 +0.543750000000000*%i; SiegelList:GiveList(z0s,cs,iMax); /* hyperbolic */ ch:0; z0h:0.843750000000000 +0.437500000000000*%i; HyperbolicList:GiveList(z0h,ch,iMax); /* escaping */ ce:-0.189093266739737 +0.677638784067832*%i; z0e:-0.289258118270603 +0.429086915059359*%i; EscapingList:GiveList(z0e,ce,iMax); /* ----------------- draw ------------ */ load(draw); draw2d( terminal = png, file_name = "distance", pic_width = 1000, /* Since Maxima 5.23, pic_width and pic_height are deprecated. */ pic_height = 500, /* See option dimensions. To get the same effect, write dimensions=[800,600] */ title = "Distance between point of orbit and fixed point ", yrange = [-0.1,1.0], points_joined =false, point_size = 0.6, point_type = filled_circle, /* */ key ="parabolic", color = red, points(ParabolicList), /* */ key ="elliptic", color = blue, points(SiegelList), /* */ key ="escaping", points_joined =true, color = black, points(EscapingList), /* */ key ="attracting", points_joined =true, color = green, points(HyperbolicList) );
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22 January 2012
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 11:40, 22 January 2012 | 1,000 × 500 (21 KB) | Soul windsurfer |
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