Questions tagged [fractals]

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61
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....
59
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2answers
7k 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 ...
51
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10answers
11k 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 ...
38
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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)", ...
28
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5answers
6k views

Making fractals with Mathematica

I recently saw this post on math.stackexchange and was curious as to how to generate the image in Mathematica. I tried the following naive approach; however, it is extremely slow. ...
25
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1answer
1k views

L-System in Mathematica

Here is some Maple code for drawing an L-System: ...
19
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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 ...
17
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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 ...
16
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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.
16
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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. ...
16
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4answers
471 views

Create a simple split tree

I am trying to create a simple split tree. The growth should be only upwards, the vertical element length constant (1), the size of the horizontal bars should be halved in each iteration and the ...
15
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2answers
679 views

I would like to create a fractal by copying, scaling and rotating the initial element

I want to create a fractal, which looks like this: This is rule 150R, which can be found in NKS, page 439. However, instead of using a cellular automaton, I want to create this fractal from a single ...
14
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2answers
643 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 ...
14
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4answers
648 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 ...
14
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2answers
815 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 ...
13
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2answers
1k views

Sampling “nice” mandelbrot sets?

I'd like to randomly sample square Mandelbrot fractals, but I'd like them to be interesting and show a "nice" section of the set: ...
13
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1answer
747 views

Animate Koch curve generation and include a transition effect

Recently, I saw two kinds of animation of Koch curve iteration generation. I don't know how to make this effect, now I can only do this ...
13
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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 ...
12
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1answer
537 views

My introduction to Compile

I am reading Fractals from the Newton-Raphson method from Peter Young's page. I've tried: ...
11
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3answers
1k views

Interactive Mandelbrot Zoomer?

I want to combine Manipulate with ManbelbrotSetPlot just to get Mathematica to give me a quick and dirty Mandelbrot Zoomer. I want to be able to single/double click on a section, and have it zoom in ...
11
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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: ...
10
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4answers
2k views

Inverted version of Sierpinski triangle

In Michael Trott's The Mathematic Guidebook for Graphics, Section 1.5.1, he first does this: ...
10
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2answers
1k 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 ...
10
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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 ...
10
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2answers
660 views

How to draw a Pythagoras tree like this

I want to draw a Pythagoras tree like the one below: But I can only do this now, and still can't do random colors. ...
10
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1answer
535 views

Random walk on a Sierpinski gasket

I am trying to simulate a random walk on a Sierpinski gasket. The best strategy i could come up with is to use Nearest point function to determine the next possible step of my walker. But this creates ...
9
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5answers
773 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
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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 ...
9
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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 ...
8
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1answer
328 views

What are the arguments supplied to ColorFunction in MandelbrotSetPlot?

On the document of MandelbrotSetPlot, it said: With ColorFunction->f, where f is a function, the argument of f is a real number in proportional to the number of ...
8
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1answer
273 views

Measuring the chaoticity (unpredictability/fractality) of a 2D plane

I have several data files containing three columns x, y, clas, where x and y are the coordinates on the configuration plane, while clas is an integer indicating the final state of the initial ...
7
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2answers
427 views

Fractal square partition

Consider the following sequence: the next are c), d) and so on. Let's assume that p1=0.2, p2=0.5, p3=0.2, p4=0.1. The question is: how to obtain (not necessarily graphically illustrated in example a)...
7
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1answer
2k views

Weierstrass function

I am trying to create plot of the Weierstrass function in Mathematica. I wonder if it's possible, when I define this function as ...
7
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1answer
165 views

What was being plotted at WWDC 2003?

At the WWDC 2003 keynote, Theodore Gray took the stage, along with Phill Schiller, and demoed Mathematica 5, comparing performance on G5 and Xeon processors. In the presentation, a 40-step fractal ...
7
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1answer
1k views

Plotting iterated function system images

I'm new not only to this forum, but to Mathematica in general, evidently. I'm running into an issue, and my best attempts at Googling solutions (and trying the search box for this forum) came up with ...
6
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3answers
295 views

How to create this doge fractal zoom?

I would like to learn how to recreate this fractal in Mathematica and make others in the same style: https://m.imgur.com/r/FractalGifs/lYEK8Cd
6
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4answers
1k views

How to draw a polygon with hue color like this one (Koch snowflake)?

I know how to construct the Koch snowflake: ...
6
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2answers
204 views

How to introduce two successive points inside the FixedPointList for each cycle?

If we want to draw the attraction basins of an iteration function of the following type $$x_{k+1}=x_k-\frac{f(x_k)}{\frac{f(x_k)-f(w_k)}{x_k-w_k}},$$ where $w_k=x_k+b f(x_k)$, $b\in R-\{0\}$, we can ...
6
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0answers
1k views

Wavelet Transform Modulus Maxima (WTMM) method

Has anyone already coded the Wavelet Transform Modulus Maxima (WTMM) method for computing the singular spectrum using multi fractal formalism in Mathematica? The goal is to analyse 1D, 2D and 3D data....
5
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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. ...
5
votes
3answers
176 views

Symmetric icons

I'm trying to replicate "symmetric icons" from this book: https://www.amazon.com/Symmetry-Chaos-Search-Pattern-Mathematics/dp/0898716721 Here is what I have so far: ...
5
votes
2answers
150 views

A box structure with a depth exceeding the maximum allowed depth was encountered

I am trying to perform the task in Mark McClure's article Parametric L-Systems and borderline fractals. I have copied his opening code on the first three pages: ...
5
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1answer
307 views

I change a single constant and the simple script suddenly takes forever to complete

I writed a code to display the Dragon Curve fractal, and I reached my goal. The algorithm works by taking the previous two points and then adding the following one by making a 90 degrees turn left or ...
4
votes
1answer
807 views

How to plot a Circles-and-Squares fractal

The Circles-and-Squares fractal is produced by iteration of the equation $\quad \quad z_{n+1}=z_n^2\ ({\rm mod}\; m)$ which results in a Moiré-like pattern: Source: Wolfram MathWorld In another ...
4
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1answer
145 views

How construct Jerusalem cube and other Menger alike 3D cubes?

Update (to clarify) My end goal is to generate Menger alike 3D cubes, as stated in the title. OP While reading the Menger cube, I found something called ...
4
votes
2answers
81 views

Speeding up RegionPlot for iterated function system fractals

This is my first post here, I have the following basic code for drawing an iterated function system fractal. It works to the third step, but then for the fourth iteration it freezes my old MacBook. I ...
4
votes
1answer
768 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 ...
4
votes
0answers
722 views

Minimalistic code challenge on Apollonian gaskets

I've been recently fascinated by the beauty, symmetry and mathematical richness of the Apollonian gaskets. So I felt myself challenged to see if it was possible to generate one in Mathematica with a ...
4
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0answers
571 views

Fractals or other patterns in the quadruple linked pendulum

This will seem like a physics question, but I'm looking for something to do in Mathematica specifically. I've successfully modeled a quadruple linked pendulum by setting up the ODEs and solving them ...
3
votes
3answers
638 views

How to create a fractal tree?

I want to create a fractal tree, using translation and rotation. Code below is working for one level, but when I try loop, it is not giving output. Code is given below: ...