Questions tagged [fractals]

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Plotting fractals in Mathematica for S iteration

Dears, I'm trying to plot the attached picture figures in Mathematica software. Let $T(z)=z-\frac{P(z)}{P^{\prime}(z)}$. The S iterative scheme is for $z_{0}$ a starting point and $y_{n}=(1-\beta_{n}...
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3 votes
2 answers
94 views

Find the central point in each Sierpinski triangle

I'm trying to do something like this for higher orders. What I've done is using a code available on internet to generate the Sierpinski points, and then TriangleCenter to obtain the medium points but ...
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1 answer
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I'm beginner and do not how to plot the Basins of attraction by the methods

For a complex polynomial $P(z)$, define $T$ by $T(z)=z-\frac{P(z)}{P^{\prime}(z)}$, where $P^{\prime}(z)$ is the first derivative of $P(z)$. We consider Newton method for finding the roots of ...
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4 votes
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How to create a Lichtenberg Figure?

I want to create a simulated Lichtenberg figure in a manner similar to this image: What is a good method to generate Lichtenberg figures? There is a very helpful post on Wolfram Community about ...
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Fractal Dimension of Lag Plot [duplicate]

Imagine I have created a lag plot from time series data. How do I get the fractal dimension of such a lag plot assuming the x-axis is x_t and the y-axis is, say x_(t-2), a lag of 2?
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2 votes
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111 views

Dense packing of disks with different radii

Let's consider a disk ($D_{1}$) whose center position is randomly generated, but the radius is fixed at $r_{1}$. A second disk ($D_{2}$) of fixed radius $r_{2}$ (with $r_{2} < r_{1}$) is randomly ...
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4 votes
1 answer
133 views

Eigenvalue and SparseArray

This the code of Hofstadter spectrum for square lattice using Mathematica ...
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5 votes
1 answer
416 views

How to create a 3D fractal flower

There is another post asking about the steps of creating a Barnsley's Fern, and it has very good answers. Now the reason I am asking this, is because I stumbled upon a post on MathOverflow which ...
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2 answers
145 views

Drawing the filled Julia set of a polynomial

Suppose I use JuliaSetPlot to draw the Julia set of a polynomial. Is there a way, assuming the set is connected, to fill in the region? My idea was to use ...
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  • 703
12 votes
4 answers
983 views

The correct way to draw this fractal

As shown in the picture, I want to draw such a fractal When the number of iterations is greater than 2, my code can't get the expected result ...
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1 answer
92 views

JuliaSetPlot - how do I achieve nicer colors?

I use the following code to generate images of Julia sets: ...
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2 votes
0 answers
63 views

JuliaSetPlot increase quality of output

For a complex dynamics class I take I want to generate a nice image of an Herman ring. I used this code to generate a first image: ...
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3 votes
1 answer
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Export high resolution 3D graphics

There is a code for a revolution of Koch Snowflake I just want to export it as an obj file (or any other 3D format) ...
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1 answer
113 views

How to obtain only the positions of the points in vertices of Sierpinski's Triangle?

Mathematica already provides a couple ways to produce the Sierpinski's Triangle, like n = 25; MatrixForm[CellularAutomaton[22, {{1}, 0}, n]] But I could not find a ...
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1 vote
1 answer
124 views

Lévy C curve fractal from a substitution systems in NKS book p.190?

How can I make the geometrical transformation described in the page 190 in the New Kind of Science book by Stephen Wolfram to produce the fractal pattern? https://www.wolframscience.com/nks/p190--...
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3 votes
1 answer
238 views

Plot Newtons Basin of Attraction using given roots

How can I use the following code without the use of solve command if I new the roots of my system of equations. My equations are a bit complex and solve command is taking to much processing time even ...
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2 votes
1 answer
175 views

Plot Julia - Fractal

I want to obtain the following figure, but I did not manage to obtain it, any suggestion? ...
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2 votes
1 answer
75 views

How to partition $[0,1]$ into $m$ equal sub-intervals and count the number of sub-intervals that intersect with my cantor set?

Suppose I define my cantor set as ...
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1 answer
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How do we list all points in the Middle $3/7$-th Cantor Set?

Suppose we were to list all points in the $3/7$th Middle Cantor set where we first remove $3/7$th of $[0,1]$: $$[0,1/7]\cup[2/7,3/7]\cup[4/7,5/7]\cup[6/7,1]$$ then $3/7$th of remaining intervals, $3/7$...
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4 votes
1 answer
509 views

Coding the Mandelbrot Set for Beginners

I'm new to Mathematica and will need some help in coding the Mandelbrot set. I don't want to use MandelbrotSetPlot since I want to understand the interior ...
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4 votes
1 answer
140 views

What are vertexes & edges returned by GraphData for "MengerSponge"?

I was messing around in Mathematica and I ended up trying this out: GraphPlot3D[GraphData[{"MengerSponge", 3}]] which produced the following (you can see a video ...
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3 votes
2 answers
97 views

How to replicate graphic output of GraphData with Graphplot?

I am trying trying to represent a Sierpinski sieve using GraphPlot. The plot I want to get is the standard representation of a Sierpinski triangle, which is the output generated by Mathematica ...
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1 vote
2 answers
131 views

Space filling function

How do I obtain the space filling function (continuous surjection $[0, 1] \to [0, 1]^2$) from a space filling curve?
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3 votes
1 answer
79 views

Euler Characteristic of MengerMesh

When I ask Mathematica to give me the Euler characteristic of MengerMesh[1, 3], it returns 16. It seems to me the 1-step Menger sponge has genus 5 and should ...
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1 vote
1 answer
54 views

How to place cuboids with a list of points?

I have a list of points found in a 3D Sierpinski triangle. How do I replace these points with Cuboids? The points come from a nested list ...
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0 votes
1 answer
77 views

How to increase the number of decimal places for this code?

How do I increase the number of decimal places for ...
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4 votes
4 answers
163 views

How do I list start and endpoints of CantorMesh?

How do I extract start and endpoints of each defined interval of iteration n of CantorMesh[n]? The furthest I can go is ...
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  • 199
6 votes
2 answers
280 views

Making a Sierpinski triangle from a Pascal triangle

I am creating triangular arrays similar to Pascal's triangle. In an answer to this post, J.M. gives the following code: ...
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3 votes
1 answer
104 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?...
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22 votes
3 answers
2k views

How to make this Dragon Curve?

I made it by another software, and met some problems to change it into MMA code. ...
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10 votes
2 answers
883 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. ...
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6 votes
3 answers
233 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: ...
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7 votes
1 answer
183 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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0 votes
0 answers
326 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 ...
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0 votes
1 answer
97 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, ...
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3 votes
1 answer
257 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 - ...
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0 votes
0 answers
77 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 ...
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7 votes
3 answers
1k 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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0 votes
1 answer
138 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. ...
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4 votes
2 answers
112 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 ...
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1 vote
0 answers
229 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 ...
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10 votes
3 answers
952 views

Simple Fractal square

I am working on a math question about infinite series, and one of the question images is below. Each new white square has an area that is 1/4 of the previous square. Always looking to learn elegant ...
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1 vote
1 answer
181 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: ...
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3 votes
3 answers
1k 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: ...
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5 votes
5 answers
509 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: ...
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0 votes
1 answer
80 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 $...
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  • 11.3k
2 votes
1 answer
135 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 ...
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  • 131
4 votes
1 answer
181 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 ...
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1 vote
0 answers
116 views

Understanding Maps and slot

Going through some old code I found this line: ...
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13 votes
2 answers
2k 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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