File:Critical Orbit for Golden Mean Quadratic Julia set.svg
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Original file (SVG file, nominally 800 × 800 pixels, file size: 263 KB)
Summary
| Description |
English: Critical Orbit, Inner and outer circle for Golden Mean Quadratic Julia set |
| Date | |
| Source | Own work |
| Author | Adam majewski |
| Other versions |
|
| SVG development |  This plot was created with Gnuplot. |
Licensing
Adam majewski, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution:
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Maxima CAS src code
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]])
);File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:59, 20 November 2011 | | 800 × 800 (263 KB) | wikimediacommons>Soul windsurfer |
