Questions tagged [fractals]
The fractals tag has no usage guidance.
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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 ...
6
votes
3answers
160 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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0answers
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Multifractality - Wolfram Code [duplicate]
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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1answer
109 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
68 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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0answers
89 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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1answer
74 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
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3answers
396 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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0answers
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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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1answer
62 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
73 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
104 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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0answers
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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
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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.
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0
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1answer
37 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 ...
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0answers
57 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
296 views
How to make an fractal text by using Mathematica?
How to make an fractal text by using Mathematica?
https://ismaelsb.shinyapps.io/FractalText/
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4answers
431 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
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2answers
405 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)...
11
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1answer
482 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
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1answer
137 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):
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1answer
177 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:
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1answer
693 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
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2
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2answers
645 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.
<...
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4answers
1k views
Inverted version of Sierpinski triangle
In Michael Trott's The Mathematic Guidebook for Graphics, Section 1.5.1, he first does this:
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5
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2answers
147 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:
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12
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3answers
520 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
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2answers
201 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 ...
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0answers
134 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
241 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
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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
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25
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1answer
926 views
1
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1answer
55 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, ...
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0answers
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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 $...
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2answers
649 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
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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 ...
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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 ...
19
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2answers
863 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 ...
9
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1answer
457 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
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1answer
682 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
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2answers
184 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
202 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
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2answers
609 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 ...
3
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4answers
269 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 ...
16
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5answers
1k views
Revolution of Koch Snowflake
How do I plot a shape made from revolving the Koch Snowflake?
I try to use RevolutionPlot3D[f, {t, t1}], but I think there is no $f$ for the Koch Snowflake.
2
votes
1answer
971 views
Basins of attraction of equilibrium points
The Henon-Heiles potential is the following
V = 1/2*(x^2 + y^2) - y*(1/3*y^2 - x^2);
which has four equilibrium points
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2
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1answer
520 views
Basins of attraction using Newton's method Part II
For the function
$F(z;Q,a) = 3z - \frac{z}{|z|^3}\left(1 + \frac{3a}{2|z|^2}\right) - Q$
the Newton iteration formula is
$z_{n+1} = z_n - \frac{F(z_n;Q,a)}{F_z(z_n,a)} = \frac{2Qz_n^4|z_n|+6z_n^3+...
2
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1answer
810 views
Basins of attraction using Newton's method
In this question Original Post the user provides a working Mathematica code which plots the basins of attraction using the Newton's iteration method. However the code works only for the function $p(z) ...
3
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1answer
796 views
How to plot fractals created with Newton's method [duplicate]
I'm quite a beginner using Mathematica. I'd like to plot the fractals of higher degree polynomials.
I have an example for z^3 - 1 which looks like this:
...
