Questions tagged [fractals]

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38
votes
4answers
6k 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)", ...
62
votes
4answers
4k 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....
12
votes
1answer
541 views

My introduction to Compile

I am reading Fractals from the Newton-Raphson method from Peter Young's page. I've tried: ...
59
votes
2answers
8k 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 ...
16
votes
5answers
1k 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.
14
votes
2answers
819 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 ...
51
votes
10answers
12k 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 ...
10
votes
2answers
2k 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 ...
25
votes
1answer
1k views

L-System in Mathematica

Here is some Maple code for drawing an L-System: ...
5
votes
6answers
2k views

Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
19
votes
2answers
1k views

Fractal basins of attraction in a Magnetic Pendulum

I am trying to write a Mathematica program that realizes a graphical approximation of the basins of attraction in a Magnetic pendulum subject to friction and gravity, in which the three magnets are ...
2
votes
1answer
1k 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 ...
14
votes
2answers
652 views

3D tree in Mathematica?

Searching the web for information about the affine transformation, I found the one page, which called my attention for the tree that show and is this but unfortunately do not give information about ...
2
votes
1answer
1k 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) ...
19
votes
3answers
1k views

How to make this Dragon Curve?

I made it by another software, and met some problems to change it into MMA code. ...
13
votes
1answer
1k 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 ...
9
votes
5answers
776 views

Sierpinski carpet with GraphData

Is this graph in the list among the so-called "standard" structures used in GraphData? However, I have not found yet anything like "Carpet" or "Sponge" in the list ...
9
votes
2answers
1k 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 ...
17
votes
6answers
1k views

Converting a Sierpinski tetrahedron to a Graph

I need a representation of a 3D Sierpinski gasket as a graph to perform some simulations on. The 2D version is included in GraphData[], but the 3D one is nowhere to ...
10
votes
2answers
2k views

Construction Steps of Barnsley's Fern

I am helping a friend with his thesis and we would like to do the following: We would like to show the construction of Barnsley's fern fractal by starting on the zeroth step with a big ellipse, then ...
9
votes
4answers
2k views

How can I make Sierpinski triangle? [duplicate]

I want to make Sierpinski triangle with method of random points. Choose p(0) inside the triangle and p(n+1)=1/2{p(n)+ one of it's vertex} I tried ...
14
votes
4answers
660 views

Using Mathematica to create an H-Tree

Can folks show me several methods I can use to draw the following fractal H-Tree? I did use Free-Form input, as: = h-fractal And got this image, which is three ...
11
votes
3answers
3k 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: ...
0
votes
0answers
114 views

Multifractal Package - Description of Multifractals

I am trying to run this Multifractal package given in the classical book of Baumann — Mathematica for Theoretical Physics II. The problem is that the code does not work, that is I have no plots. In my ...
4
votes
1answer
778 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
943 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
591 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
741 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
378 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 ...
0
votes
1answer
118 views

Help with debugging my code [closed]

In order to descrive the multifractal behaviour of a set, Baumann provides a code based on the functions Dq and Tau, given below. ...