https://github.com/czlee/cme257hw4czlee

CME 257 Homework 4. Tool for visualizing Julia sets.
https://github.com/czlee/cme257hw4czlee

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CME 257 Homework 4. Tool for visualizing Julia sets.

• Host: GitHub
• URL: https://github.com/czlee/cme257hw4czlee
• Owner: czlee
• License: other
• Created: 2015-10-15T20:02:58.000Z (almost 9 years ago)
• Default Branch: master
• Last Pushed: 2015-10-15T22:05:27.000Z (almost 9 years ago)
• Last Synced: 2023-03-23T23:57:55.621Z (over 1 year ago)
• Language: Julia
• Size: 109 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
# cme257hw4czlee: Julia sets

This package contains one function:

    juliaset{T<:Real}(R::Function, x::AbstractVector{T}, y::AbstractVector{T},

            n_iter=50, escape_tol=1e10)

`R(z)` is expected to be a rational function of the form `P(z)/Q(z)`, where `P`

and `Q` are polynomials in `z` without common divisors.

The function returns an `length(x)`-by-`length(y)` matrix whose `[i,j]`-th

element denotes the number of iterations it took the norm of `z[i,j] = x[i] +

im*y[j]` to exceed `escape_tol`, where in each iteration `z[i,j]` is replaced by

`R(z[i,j])`. If it takes longer than `n_iter` iterations, the relevant element

of the returned matrix will be `n_iter+1`.

## Example

``` julia

using cme257hw4czlee

using PyPlot

R = z -> (5z^4 + 3z^2 + z) / (z^2 - 9z + 3)

x = -5:0.025:5

y = -5:0.025:5

J = juliaset(R, x, y);

matshow(J)

```