I am trying to make a program in turtle that creates a Lyapunov fractal. However, as using timeit shows, this should take around 3 hours to complete, 1.5 if I compromise resolution (N).
import turtle as t; from math import log; from timeit import default_timer as dt
t.setup(2000,1000,0); swid=t.window_width(); shei=t.window_height(); t.up(); t.ht(); t.tracer(False); t.colormode(255); t.bgcolor('pink')
def lyapunov(seq,xmin,xmax,ymin,ymax,N,tico):
truseq=str(bin(seq))[2:]
for x in range(-swid//2+2,swid//2-2):
tx=(x*(xmax-xmin))/swid+(xmax+xmin)/2
if x==-swid//2+2:
startt=dt()
for y in range(-shei//2+11,shei//2-1):
t.goto(x,y); ty=(y*(ymax-ymin))/shei+(ymax+ymin)/2; lex=0; xn=prevxn=0.5
for n in range(1,N+1):
if truseq[n%len(truseq)]=='0': rn=tx
else: rn=ty
xn=rn*prevxn*(1-prevxn)
prevxn=xn
if xn!=1: lex+=(1/N)*log(abs(rn*(1-2*xn)))
if lex>0: t.pencolor(0,0,min(int(lex*tico),255))
else: t.pencolor(max(255+int(lex*tico),0),max(255+int(lex*tico),0),0)
t.dot(size=1); t.update()
if x==-swid//2+2:
endt=dt()
print(f'Estimated total time: {(endt-startt)*(swid-5)} secs')
#Example: lyapunov(2,2.0,4.0,2.0,4.0,10000,100)
I attempted to use yield but I couldn't figure out where it should go.
On my slower machine, I was only able to test with a tiny N (e.g. 10) but I was able to speed up the code about 350 times. (Though this will be clearly lower as N increases.) There are two problems with your use of update()
. The first is you call it too often -- you should outdent it from the y
loop to the x
loop so it's only called once on each vertical pass. Second, the dot()
operator forces an automatic update()
so you get no advantage from using tracer()
. Replace dot()
with some other method of drawing a pixel and you'll get back the advantage of using tracer()
and update()
. (As long as you move update()
out of innermost loop as I noted.)
My rework of your code where I tried out these, and other, changes:
from turtle import Screen, Turtle
from math import log
from timeit import default_timer
def lyapunov(seq, xmin, xmax, ymin, ymax, N, tico):
xdif = xmax - xmin
ydif = ymax - ymin
truseq = str(bin(seq))[2:]
for x in range(2 - swid_2, swid_2 - 2):
if x == 2 - swid_2:
startt = default_timer()
tx = x * xdif / swid + xdif/2
for y in range(11 - shei_2, shei_2 - 1):
ty = y * ydif / shei + ydif/2
lex = 0
xn = prevxn = 0.5
for n in range(1, N+1):
rn = tx if truseq[n % len(truseq)] == '0' else ty
xn = rn * prevxn * (1 - prevxn)
prevxn = xn
if xn != 1:
lex += 1/N * log(abs(rn * (1 - xn*2)))
if lex > 0:
turtle.pencolor(0, 0, min(int(lex * tico), 255))
else:
lex_tico = max(int(lex * tico) + 255, 0)
turtle.pencolor(lex_tico, lex_tico, 0)
turtle.goto(x, y)
turtle.pendown()
turtle.penup()
screen.update()
if x == 2 - swid_2:
endt = default_timer()
print(f'Estimated total time: {(endt - startt) * (swid - 5)} secs')
screen = Screen()
screen.setup(2000, 1000, startx=0)
screen.bgcolor('pink')
screen.colormode(255)
screen.tracer(False)
swid = screen.window_width()
shei = screen.window_height()
swid_2 = swid//2
shei_2 = shei//2
turtle = Turtle()
turtle.hideturtle()
turtle.penup()
turtle.setheading(90)
lyapunov(2, 2.0, 4.0, 2.0, 4.0, 10, 100)
screen.exitonclick()