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50
votes
4answers
3k views

Speeding up this fractal-generating code

I used the code below (which is a sample from this gist containing more similar code) in my answer to my own question about Mandelbrot-like sets for functions other than the simple quadratic on Math....
26
votes
4answers
4k views

How to draw Fractal images of iteration functions on the Riemann sphere?

Prof. McClure, in the work "M. McClure, Newton's method for complex polynomials. A preprint version of a “Mathematical graphics” column from Mathematica in Education and Research, pp. 1–15 (2006)", ...
47
votes
1answer
4k views

Measuring fractal dimension of natural objects from digital images

This is a useful topic. A college physics lab, medical diagnostics, urban growth, etc. - there is a lot of applications. On this site by Paul Bourke about Google Earth fractals we can get a high ...
43
votes
10answers
9k views

Generating a Sierpinski carpet

I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
13
votes
2answers
657 views

How can I compile this function

I want to simplify my function f1 to f2, but f2 can't be compiled. How can I make it ...
15
votes
5answers
629 views

Revolution of Koch Snowflake

How do I plot a shape made from revolving the Koch Snowflake? I try to use RevolutionPlot3D[f, {t, t1}], but I think there is no $f$ for the Koch Snowflake.
7
votes
2answers
1k views

Manipulating plot of random iterated function system fractal

I'm generating the Sierpinski Gasket by implementing a chaos game in Mathematica. What I'd like to do is create an interactive manipulation with a slider, whereby moving it forward, plots all the ...
0
votes
1answer
153 views

Basins of attraction using Newton's method

In this question Original Post the user provides a working Mathematica code which plots the basins of attraction using the Newton's iteration method. However the code works only for the function $p(z) ...
8
votes
1answer
281 views

How to make a Nebulabrot?

A Nebulabrot is a generalization of the Buddhabrot, a fractal rendering technique related to the Mandelbrot set that sort of looks like a meditating buddha. The Buddhabrot rendering technique was ...
1
vote
1answer
259 views

Basins of attraction of equilibrium points

The Henon-Heiles potential is the following V = 1/2*(x^2 + y^2) - y*(1/3*y^2 - x^2); which has four equilibrium points ...
11
votes
3answers
2k views

Poor rendering of fractals

Could someone explain why I get those ugly graphics .. ..trying to use fractals in mathematica 8 ? I'd also like to know if it is possible to draw 2D fractals in Mathematica My configuration is:...
8
votes
1answer
612 views

Computing the Hurst exponent or fractal dimension of fractional Brownian motion

The Hurst exponent is related to the fractal dimension by noticing that the fractal dimension $D$ is equal to $2-H$, where $d$ is the intrinsic dimension and $H$ is the Hurst exponent, for 1-D ...
4
votes
1answer
382 views

How do I built a zoomable Koch curve?

I'm new to Mathematica and my goal is to write a simple program in order to demonstrate self-similarity of the Koch curve by zooming in. Here is a good example of what I mean (it's a Java applet). I ...
3
votes
1answer
182 views

How to plot fractals created with Newton's method [duplicate]

I'm quite a beginner using Mathematica. I'd like to plot the fractals of higher degree polynomials. I have an example for z^3 - 1 which looks like this: ...
2
votes
1answer
138 views

Basins of attraction using Newton's method Part II

For the function $F(z;Q,a) = 3z - \frac{z}{|z|^3}\left(1 + \frac{3a}{2|z|^2}\right) - Q$ the Newton iteration formula is $z_{n+1} = z_n - \frac{F(z_n;Q,a)}{F_z(z_n,a)} = \frac{2Qz_n^4|z_n|+6z_n^3+...
2
votes
1answer
358 views

calculating a sequence of functions using iteration

I am trying to compute a sequence of functions using iteration and keep running into problems trying to use built in looping commands because of the recursive nature of the definition. The code below (...
1
vote
1answer
200 views

multiple generators for iterative construction of fractal

The code below is an attempt to use more than one generator (in this case two) to generate a fractal using the standard iterative procedure involving generators. Only the first two stages of the ...