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47
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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 ...
47
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 ...
24
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)", ...
42
votes
10answers
8k 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
630 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 ...
10
votes
4answers
493 views

Revolution of Koch Snowflake

How to plot shape which made from revolution of the Koch Snowflake? I try to use $RevolutionPlot3D[f,\lbrace {t,t_1} \rbrace]$, but I think there is no $f$ for Koch Snowflake. Sorry for my ...
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
111 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) ...
1
vote
1answer
226 views

Combining Mandelbrot and Monte Carlo

I'm trying to combine plotting a Mandelbrot set with Monte Carlo randomization to plot an equation using random points for complex number z, for the function $z^3-2z+2=0$. Below is the code I have ...
1
vote
1answer
95 views

FindProcessParameters for Fractional Brownian Motion Returns Error

I have the following data: ...
8
votes
1answer
220 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
215 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 ...
7
votes
1answer
541 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
340 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
113 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
121 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)} = ...
2
votes
1answer
324 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
178 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 ...