The usual scheme for Newton’s method is . But what if we just choose some random for ?

Set

Now, as far as differential equations go, solving

is pretty tricky.

But I can still generate a fractal from it:

The usual scheme for Newton’s method is . But what if we just choose some random for ?

Set

Now, as far as differential equations go, solving

is pretty tricky.

But I can still generate a fractal from it:

suppose you’re doing a Newton’s method fractal of , and you forget the derivative and use instead

I saw solving on m.se today, and decided that it was ripe for a Newton’s method fractal, so, here you go:

It uses the following python code:

#!/usr/bin/python

from mpmath import *

import pylab

def g(z,x):

return x*(z**x) + x + 1

def newt(z):

x = z

for i in range(1,30):

x = x - g(z,x)/((z**x)*(1.0+x*fp.log(z))+1.0)

return x

`fp.cplot(lambda z: newt(z), [-5.0,5.0], [-5.0,5.0], verbose=True, points=800000)
`