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Questions tagged [fractals]

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13 votes
4 answers
386 views

Reproduce the annulus fractal

I've made some attempts, but I don't know how to set the color and thickness of the circle. ...
vector's user avatar
  • 201
13 votes
3 answers
1k views

Diploria labyrinthiformis - can we reproduce Ernst Haeckel's drawing of a brain coral?

Ernst Haeckel (1834 - 1919) was a German philosopher, physician, artist and professor of zoology at the University of Jena. He promoted and popularised Charles Darwin's work in Germany. Haeckel (left)...
eldo's user avatar
  • 75.2k
18 votes
3 answers
957 views

How to weave Anni Albers Red Meander carpet?

Anni Albers (1899 - 1994) was a German artist regarded as one of the most influential textile designers of the 20th century. Since 1931 Albers was head of the Bauhaus weaving workshops in Dessau and ...
eldo's user avatar
  • 75.2k
12 votes
9 answers
2k views

How can I draw sequence of these fractal squares?

For the first square, I tried Graphics[{Green, Rectangle[{0, 0}, {3, 3}]}]
Thuy Nguyen's user avatar
  • 1,097
8 votes
2 answers
539 views

How to recursively subdivide a quadrilateral?

I have the following problem which is most easily described by this diagram: We start off with a quadrilateral, not necessarily a square, with four fixed points, here represented in green. We have a ...
flinty's user avatar
  • 25.5k
0 votes
1 answer
106 views

I want to graph a heatmap for three parameter data

I want to plot a heatmap where $x$ varies from $0.1$ to $1$, $y$ varies $0.1$ to $1$, and a third parameter representing image generation times for different $(x,y)$ will be the input to a ...
arifeen ahmed's user avatar
0 votes
1 answer
120 views

How can I nest a complex function?

I am examining the mandelbrot set so I need to iterate the function f[z_Complex, c_] := (z)^2 + c Besides, I want to choose the complex numbers dynamically from ...
Süleyman Küçük's user avatar
1 vote
0 answers
67 views

How to get the closest point from the known point to a fractal tree?

Given a known point, how to analytically find the nearest point from the point to the fractal tree? The fractal tree code: ...
kathy's user avatar
  • 11
0 votes
1 answer
352 views

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}...
Junaid's user avatar
  • 161
3 votes
2 answers
174 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 ...
Lucas Lopes's user avatar
11 votes
1 answer
520 views

Speediest Julia Set "By Hand"

While being aware of the built-in command, I would like to show my students how the Julia set is actually generated. The code I came up with is slow, even though I am quite happy with the picture it ...
Matthias's user avatar
  • 353
0 votes
1 answer
233 views

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 ...
Junaid's user avatar
  • 161
4 votes
0 answers
516 views

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 ...
Peter Burbery's user avatar
2 votes
0 answers
161 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 ...
Tony Ravina's user avatar
4 votes
1 answer
156 views

Eigenvalue and SparseArray

This the code of Hofstadter spectrum for square lattice using Mathematica ...
Yduog chan's user avatar
5 votes
1 answer
710 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 ...
polfosol's user avatar
  • 952
0 votes
2 answers
258 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 ...
math's user avatar
  • 773
12 votes
5 answers
1k 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 ...
expression's user avatar
  • 5,652
0 votes
1 answer
112 views

JuliaSetPlot - how do I achieve nicer colors?

I use the following code to generate images of Julia sets: ...
Arji's user avatar
  • 1,134
2 votes
0 answers
86 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: ...
Arji's user avatar
  • 1,134
3 votes
1 answer
387 views

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) ...
vito's user avatar
  • 8,958
0 votes
1 answer
163 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 ...
Lucas Lopes's user avatar
1 vote
1 answer
199 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--...
Quantum Fields's user avatar
3 votes
1 answer
584 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 ...
Atique Khan's user avatar
2 votes
1 answer
290 views

Plot Julia - Fractal

I want to obtain the following figure, but I did not manage to obtain it, any suggestion? ...
Halsey12's user avatar
2 votes
1 answer
129 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 ...
Arbuja's user avatar
  • 71
0 votes
1 answer
103 views

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, $3/7$...
Arbuja's user avatar
  • 71
8 votes
1 answer
1k 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 ...
Hannes Schumacher's user avatar
4 votes
1 answer
167 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 ...
EllipticalInitial's user avatar
3 votes
2 answers
135 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 ...
Carlos_San's user avatar
1 vote
2 answers
182 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?
user avatar
3 votes
1 answer
120 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 ...
Ruben's user avatar
  • 131
1 vote
1 answer
81 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 ...
Brian Stephenson's user avatar
0 votes
1 answer
114 views

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

How do I increase the number of decimal places for ...
Arbuja's user avatar
  • 71
4 votes
4 answers
172 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 ...
Arbuja's user avatar
  • 71
6 votes
2 answers
433 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: ...
Descartes Before the Horse's user avatar
3 votes
1 answer
129 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?...
ryan.axiom's user avatar
26 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. ...
AsukaMinato's user avatar
  • 9,948
12 votes
2 answers
2k 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. ...
A little mouse on the pampas's user avatar
6 votes
3 answers
260 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: ...
Bart Snapp's user avatar
7 votes
1 answer
192 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 ...
M.R.'s user avatar
  • 31.6k
0 votes
2 answers
840 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 ...
Muhammad Imran's user avatar
0 votes
1 answer
159 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, ...
Varun Vejalla's user avatar
3 votes
1 answer
352 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 - ...
Varun Vejalla's user avatar
0 votes
0 answers
84 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 ...
MostafaMV's user avatar
  • 453
7 votes
3 answers
2k 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
user5601's user avatar
  • 3,655
0 votes
1 answer
142 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. ...
Spook82's user avatar
  • 95
5 votes
2 answers
147 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 ...
manifoldcurious's user avatar
1 vote
0 answers
276 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 ...
Spook82's user avatar
  • 95
10 votes
3 answers
1k 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 ...
Tom De Vries's user avatar
  • 3,780