Questions tagged [fractals]

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16
votes
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
661 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
votes
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
votes
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 ...
0
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0answers
81 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 ...
0
votes
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
votes
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 - ...
0
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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
votes
3answers
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
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
vote
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: ...
3
votes
3answers
640 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: ...
2
votes
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
votes
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
votes
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
votes
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 ...
1
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0answers
86 views

Understanding Maps and slot

Going through some old code I found this line: ...
13
votes
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: ...
1
vote
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
votes
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 ...
2
votes
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
votes
1answer
408 views

How to make an fractal text by using Mathematica?

How to make an fractal text by using Mathematica? https://ismaelsb.shinyapps.io/FractalText/
16
votes
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 ...
7
votes
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)...
14
votes
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 ...
2
votes
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): ...
1
vote
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
votes
1answer
749 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 ...
2
votes
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. <...
10
votes
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: ...
5
votes
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: ...
14
votes
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 ...
0
votes
2answers
272 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
vote
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
votes
1answer
273 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 ...
9
votes
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 ...
25
votes
1answer
1k views

L-System in Mathematica

Here is some Maple code for drawing an L-System: ...
1
vote
1answer
61 views

Label & enlarge endpoints of 1-dimensional CantorMesh? (11.1)

Version 11.1 introduces the function CantorMesh. I'm interested in using it to indicate how the classical "Cantor middle-third set" is formed. In the following, ...
0
votes
0answers
151 views

Highlight gaps in the Carotid-Kundalini Fractal

Gaps in Fractal Land occur whenever $$x\cos^{-1}x=2\pi\frac{p}{q}$$ for $p$ and $q$ realatively prime integers.At such points $x$, the functions assume the $⌈(q+1)/2⌉$ values $\cos(2\pi/q)$ for $...
15
votes
2answers
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 ...
10
votes
2answers
1k views

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 ...
17
votes
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 ...
19
votes
2answers
1k views

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 ...
10
votes
1answer
537 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 ...
2
votes
1answer
753 views

Fractal plotting for the Collatz fractal

I have the following equation: f[z_] := 1/4 (2 + 7 z - (2 + 5 z) Cos[Pi*z]) I want to map this on the imaginary plane such that if it converges under iterations ...
6
votes
2answers
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 ...
1
vote
1answer
241 views

Coordinates of the centers of the triangles composing a Koch snowflake [duplicate]

How do I obtain the coordinates of the centers of triangles composing the Koch snowflake?
3
votes
2answers
687 views

Mandelbrot set—efficiently iterate over a list of initial points

OP edit: This is a Mathematica-specific question about an approach it attempted for a fractal visualization problem described HERE. I'm using the Mandelbrot set there and here as an example, but the ...