#8423: fractals: add code to plot julia sets
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Reporter: was | Owner: sdietzel
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.3.4
Component: fractals | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by mhampton):
Here's an iterated function system example (the fern):
{{{
def fern(x,y):
"""
An iterated function system whose orbit traces out
a fern shape.
INPUT:
x,y - numerical scalars
OUTPUT:
a 2-component list of new x and y values.
"""
r = random()
if r<.01:
return [0,.16*y]
elif r < .08:
return [.2*x-.26*y, .23*x+.22*y+1.6]
elif r < .15:
return [-.15*x+.28*y, .26*x+.24*y+.44]
else:
return [.85*x+.04*y,-.04*x+.85*y+1.6]
def fern_orbit(n):
"""
Returns a trajectory of length n of the fern
iterated function system.
INPUT:
n - an integer, the length of the trajectory
OUTPUT:
a list of 2-component lists
EXAMPLE:
sage: show(points(fern_orbit(10000),pointsize=1),axes=False)
"""
traj = [[0,0]]
for i in range(n):
nt = fern(traj[-1][0],traj[-1][1])
traj.append(nt)
return traj
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8423#comment:4>
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