# Questions tagged [fractals]

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### 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....
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 ...
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 ...
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)", ...
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### 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. ...
1k views

### L-System in Mathematica

Here is some Maple code for drawing an L-System: ...
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### 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 ...
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 ...
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.
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### How to make this Dragon Curve?

I made it by another software, and met some problems to change it into MMA code. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
537 views

### My introduction to Compile

I am reading Fractals from the Newton-Raphson method from Peter Young's page. I've tried: ...
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 ...
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### 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: ...
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### Inverted version of Sierpinski triangle

In Michael Trott's The Mathematic Guidebook for Graphics, Section 1.5.1, he first does this: ...
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### 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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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)...
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### 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 ...
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 ...
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### 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 ...
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
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### How to draw a polygon with hue color like this one (Koch snowflake)?

I know how to construct the Koch snowflake: ...
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 ...
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### 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....
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### 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. ...
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### 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: ...
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### 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: ...
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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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 ...
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 ...