Questions tagged [fractals]
The fractals tag has no usage guidance.
126
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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 ...
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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 ...
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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 ...
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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:
...
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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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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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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 ...
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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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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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2
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0
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142
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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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Eigenvalue and SparseArray
This the code of Hofstadter spectrum for square lattice using Mathematica
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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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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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4
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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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JuliaSetPlot - how do I achieve nicer colors?
I use the following code to generate images of Julia sets:
...
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80
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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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1
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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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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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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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1
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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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1
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261
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Plot Julia - Fractal
I want to obtain the following figure, but I did not manage to obtain it, any suggestion?
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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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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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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 ...
4
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1
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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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111
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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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163
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Space filling function
How do I obtain the space filling function (continuous surjection $[0, 1] \to [0, 1]^2$) from a space filling curve?
user66704
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110
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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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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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94
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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
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168
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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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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
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123
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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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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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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.
...
6
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3
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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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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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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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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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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 - ...
- 147
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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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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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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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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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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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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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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
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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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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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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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