## Friday, July 12, 2013

### Hopalong fractals

Have you ever wondered what happen if you pick a point (x0,y0) and compute hundreds of point using these equations?

Well, you get a hopalong fractal.
Let's plot this fractal using Pylab. The following function computes n points using the equations above:
```from __future__ import division
from numpy import sqrt,power

def hopalong(x0,y0,n,a=-55,b=-1,c=-42):
def update(x,y):
x1 = y-x/abs(x)*sqrt(abs(b*x+c))
y1 = a-x
return x1,y1
xx = []
yy = []
for _ in xrange(n):
x0,y0 = update(x0,y0)
xx.append(x0)
yy.append(y0)
return xx,yy
```
and this snippet computes 40000 points starting from (-1,10):
```from pylab import scatter,show, cm, axis
from numpy import array,mean
x = -1
y = 10
n = 40000
xx,yy = hopalong(x,y,n)
cr = sqrt(power(array(xx)-mean(xx),2)+power(array(yy)-mean(yy),2))
scatter(xx, yy, marker='.', c=cr/max(cr),
edgecolor='w', cmap=cm.Dark2, s=50)
axis('equal')
show()
```
Here we have one of the possible hopalong fractals:

Varying the starting point and the values of a, b and c we have different fractals. Here are some of them:

1. Thank you for sharing your method. it,s great. Tesla and Elon Musk
2. 1. 