# Tagged Questions

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2answers
263 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 ...
5answers
657 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.
1answer
4k views

### Measuring fractal dimension of natural objects from digital images

This is a useful topic. A college physics lab, medical diagnostics, urban growth, etc. - there is a lot of applications. On this site by Paul Bourke about Google Earth fractals we can get a high ...
1answer
231 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 ...
1answer
159 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 ...
1answer
72 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?
2answers
124 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 ...
10answers
9k views

### Generating a Sierpinski carpet

I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
2answers
360 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 ...
1answer
270 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 ...
1answer
140 views

1answer
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### 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: ...
2answers
497 views

### Sierpinski carpet with GraphData

Is this graph in the list among the so-called "standard" structures used in GraphData? However, I have not found, yet, anything like "Carpet" or "Sponge" in the ...
1answer
283 views

### I change a single constant and the simple script suddenly takes forever to complete

I writed a code to display the Dragon Curve fractal, and I reached my goal. The algorithm works by taking the previous two points and then adding the following one by making a 90 degrees turn left or ...
1answer
300 views

### How to make a Nebulabrot?

A Nebulabrot is a generalization of the Buddhabrot, a fractal rendering technique related to the Mandelbrot set that sort of looks like a meditating buddha. The Buddhabrot rendering technique was ...
1answer
427 views

### Plotting iterated function system images

I'm new not only to this forum, but to Mathematica in general, evidently. I'm running into an issue, and my best attempts at Googling solutions (and trying the search box for this forum) came up with ...
0answers
490 views

### Wavelet Transform Modulus Maxima (WTMM) method

Has anyone already coded the Wavelet Transform Modulus Maxima (WTMM) method for computing the singular spectrum using multi fractal formalism in Mathematica? The goal is to analyse 1D, 2D and 3D data....
2answers
1k views

### Manipulating plot of random iterated function system fractal

I'm generating the Sierpinski Gasket by implementing a chaos game in Mathematica. What I'd like to do is create an interactive manipulation with a slider, whereby moving it forward, plots all the ...
0answers
79 views

### How to efficiently find period orbits in a series defined by recurrence relation?

I have a series defined as $z_{n+1} = z_n^2 + c$, which is the series for the Mandelbrot set. I have defined it, in order to plot the set, as ...
2answers
516 views

### Interactive Mandelbrot Zoomer?

I want to combine Manipulate with ManbelbrotSetPlot just to get Mathematica to give me a quick and dirty Mandelbrot Zoomer. I want to be able to single/double click on a section, and have it zoom in ...
0answers
104 views

### Do not like quality of graphics when exported by Mathematica 9 [closed]

I have been using Mathematica 9 to generate images of fractals for some time, and I noticed an uncomfortable phenomenon when I export the fractal image into a PDF. The lines get thick so that the ...
0answers
314 views

### Minimalistic code challenge on Apollonian gaskets

I've been recently fascinated by the beauty, symmetry and mathematical richness of the Apollonian gaskets. So I felt myself challenged to see if it was possible to generate one in Mathematica with ...
1answer
252 views

### Combining Mandelbrot and Monte Carlo

I'm trying to combine plotting a Mandelbrot set with Monte Carlo randomization to plot an equation using random points for complex number z, for the function $z^3-2z+2=0$. Below is the code I have ...
1answer
235 views

### 3D Vicsek Fractal Notebook

Can I get a link to a notebook that explores this fractal structure? I am specifically asking for a url to a Mathematica notebook that generates and / or visualizes this type of fractal. If that ...
3answers
533 views

### How to draw a polygon with hue color like this one (Koch snowflake)?

I know how to construction Koch snowflake ...
1answer
162 views

### What are the arguments supplied to ColorFunction in MandelbrotSetPlot?

On the document of MandelbrotSetPlot, it said: With ColorFunction->f, where f is a function, the argument of f is a real number in proportional to the number of ...
0answers
283 views

### Fractals or other patterns in the quadruple linked pendulum

This will seem like a physics question, but I'm looking for something to do in Mathematica specifically. I've successfully modeled a quadruple linked pendulum by setting up the ODEs and solving them ...
1answer
101 views

### FindProcessParameters for Fractional Brownian Motion Returns Error

I have the following data: ...
1answer
370 views

### How to plot a Circles-and-Squares fractal

The Circles-and-Squares fractal is produced by iteration of the equation $\quad \quad z_{n+1}=z_n^2\ ({\rm mod}\; m)$ which results in a Moiré-like pattern: Source: Wolfram MathWorld In ...
1answer
620 views

### Computing the Hurst exponent or fractal dimension of fractional Brownian motion

The Hurst exponent is related to the fractal dimension by noticing that the fractal dimension $D$ is equal to $2-H$, where $d$ is the intrinsic dimension and $H$ is the Hurst exponent, for 1-D ...
6answers
2k views

### Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
1answer
287 views

### Better code for two variable fractal interpolation functions

I am trying to write code for 2-variable fractal interpolation functions using two iterated function systems and two starting functions (both $y(x)=x$) which creates a sequence of piecewise defined ...
1answer
201 views

### multiple generators for iterative construction of fractal

The code below is an attempt to use more than one generator (in this case two) to generate a fractal using the standard iterative procedure involving generators. Only the first two stages of the ...
1answer
207 views

### Optimization of power tower fractal generator [closed]

I tried to optimize the code for generating power tower fractals from here. As the author suggested, I tried to memorize the points already tested in a list. Here is my code : ...
1answer
387 views

### How do I built a zoomable Koch curve?

I'm new to Mathematica and my goal is to write a simple program in order to demonstrate self-similarity of the Koch curve by zooming in. Here is a good example of what I mean (it's a Java applet). I ...
1answer
694 views

### How to generate this fractal-like 3D distribution of points in Mma 7.0?

I would like to produce some 3D distributions of points using Mathematica 7.0, that look like the picture below : How could I do that ? What are your suggestions ? What Mma 7 codes could do a ...
4answers
3k views

### Speeding up this fractal-generating code

I used the code below (which is a sample from this gist containing more similar code) in my answer to my own question about Mandelbrot-like sets for functions other than the simple quadratic on Math....
3answers
2k views

### Poor rendering of fractals

Could someone explain why I get those ugly graphics .. ..trying to use fractals in mathematica 8 ? I'd also like to know if it is possible to draw 2D fractals in Mathematica My configuration is:...
1answer
360 views

### calculating a sequence of functions using iteration

I am trying to compute a sequence of functions using iteration and keep running into problems trying to use built in looping commands because of the recursive nature of the definition. The code below (...
2answers
661 views

### How can I compile this function

I want to simplify my function f1 to f2, but f2 can't be compiled. How can I make it ...
4answers
4k views

### How to draw Fractal images of iteration functions on the Riemann sphere?

Prof. McClure, in the work "M. McClure, Newton's method for complex polynomials. A preprint version of a “Mathematical graphics” column from Mathematica in Education and Research, pp. 1–15 (2006)", ...
5answers
5k views

### Making fractals with Mathematica

I recently saw this post on math.stackexchange and was curious as to how to generate the image in Mathematica. I tried the following naive approach; however, it is extremely slow. ...