Questions tagged [fractals]

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2
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1answer
46 views

How to turn a collection of contour lines into a printable object (mesh, etc)?

Inspired by Henry Segerman's developing fractal curves, I decided to try to convince Mathematica to do something similar. The inspiration for cf, f, and g below came from How to make this Dragon Curve?...
18
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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. ...
10
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2answers
666 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. ...
5
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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: ...
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 ...
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0answers
83 views

Hofstadter Butterfly for graphene

I am trying to extend the Harper equation from two dimensional square lattice to monolayer graphene by using mathematica. For square lattice the code is given here "Poor rendering of fractals". The ...
14
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4answers
650 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 ...
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 ...
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 ...
0
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1answer
54 views

Using KochCurve in order to create a fractal

I am having trouble creating a Koch curve using the function KochCurve in Mathematica. What I want to create is something like this. However, what I end up with, ...
3
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1answer
115 views

Area of Generalized Koch Snowflake

I asked on the Math Stack Exchange here how I could find the area of a "generalized Koch snowflake". An $n$th generalized Koch snowflake, in my case, is formed almost the same as the Koch snowflake - ...
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 ...
61
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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....
2
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1answer
533 views

How to plot on complex plane with Mandelbrot set

I essentially want to treat the Mandelbrot set plot as a normal plot so that I can plot arrows and points on top of it. This is what I want to do but it gives me an error: ...
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0answers
60 views

N-dimensional Moore Curve

How do I implement an $N$-dimensional Moore Curve in Mathematica? It is known that a Moore curve of order $P$ in N-dimensions can be made of $2^{N}$ Hilbert curves of order $P-1$ arranged on the ...
6
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3answers
297 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
0
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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. ...
4
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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 ...
0
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0answers
113 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 ...
1
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1answer
92 views

Reiterative Graphics- Fractals and Isometries

I am trying to reiterate a program on mathematica. Say, I begin with a circle partitioned into 3 symmetric regions. The code is below: ...
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 ...
3
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3answers
641 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: ...
8
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1answer
329 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 ...
2
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0answers
95 views

How to achieve this fractal image transformation?

The app MirrorLab on Android has a very interesting Julia Effect, and I'd like to recreate this effect in Mathematica. Here are some examples of input images and their outputs: ...
0
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1answer
64 views

Testing a description of the Cantor ternary set

The Cantor ternary set (aka the Cantor discontinuum) is, as usual, the set $K = \bigcap_{n=0}^{\infty} K_{n}$ where $K_{0} = [0, 1]$, the closed unit interval, and where for each $n \geq 1$ the set $...
2
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1answer
96 views

Strahler order of a graph(drainage network)

How can I find the Strahler order of a drainage network in Mathematica? For example the link created by joining links of order $i$ and $j$ is given by $k=max(i,j,Int\frac{1}{2}(i+j))$. The image of ...
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 ...
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 ...
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0answers
86 views

Understanding Maps and slot

Going through some old code I found this line: ...
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)", ...
2
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2answers
843 views

Basins of attraction when using Newton's method to solve $x^3-1 = 0$

I created Newton fractal plot for x^3 - 1 and would like to know where did I go wrong. I know I could have just copied the code but that would not have been fun. <...
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: ...
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0answers
142 views

How to show the cross section of a 3D MengerMesh?

I want to show a gif like this: Menger Sponge Slices I think I can ues a big Cuboid to cut the MengerMesh. ...
0
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1answer
42 views

Slowly Varing Color in the Listplot (by iteration, time or next data point)

I am having little trouble with coloring the list plot. I want to vary the color slowly. For example, if I have data {0,1,2,3,5,7,8,9,7,5,2,1,3,5} I want it to ...
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 ...
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 ...
2
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0answers
60 views

How MandelbrotSetBoettcher function is computed?

Boettcher function is a solution of Boettcher's functional equation, so in case of complex quadratic map: $B(f(z)) = (B(z))^2$ where: B is Boettchers function f is complex quadratic map There is a ...
2
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1answer
409 views

How to make an fractal text by using Mathematica?

How to make an fractal text by using Mathematica? https://ismaelsb.shinyapps.io/FractalText/
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: ...
2
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1answer
153 views

How to make this tree using AnglePath?

Here is a Python turtle code for making a fractral tree, I had translation it to mathematica code(see Make a series of points curl): ...
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)...
3
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4answers
338 views

cantor set intervals

I have been trying to figure out how to get the values for the limits of the Cantor set intervals (see here). The formulas that i could find only gave the interval themselves but what i need is only ...
1
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1answer
202 views

How to implement fractal flames in Mathematica?

See Wiki and the description here . Here is my attempt to realize the pseudocode in p.3: ...
13
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1answer
750 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 ...
5
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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: ...
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 ...
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 ...
0
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2answers
274 views

Tag Times in polynomial is Protected [duplicate]

I want to create a list of polynomials that start with 1 and have additional terms that are negative ie 1-x,1-x-x^2,1-x^9, etc to create a cool fractal by numerically solving them and plotting the ...
1
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0answers
177 views

Julia set on Riemann sphere [duplicate]

How to draw Julia sets of rational functions on Riemann sphere, the inbuilt mathematica command draws it on complex plane. Edit: My question is marked a duplicate by many learned people but when I ...
8
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1answer
274 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 ...