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1
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1answer
44 views

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

Let's suppose we have a Koch snowflake of arbitrary initial side length $a$, and a Cartesian coordinate system whose center coincide with the center of Koch snowflake, as shown in the figure. How ...
3
votes
3answers
282 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 ...
10
votes
4answers
491 views

Revolution of Koch Snowflake

How to plot shape which made from revolution of the Koch Snowflake? I try to use $RevolutionPlot3D[f,\lbrace {t,t_1} \rbrace]$, but I think there is no $f$ for Koch Snowflake. Sorry for my ...
1
vote
1answer
213 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 ...
2
votes
1answer
119 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)} = ...
0
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1answer
111 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
votes
1answer
113 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: ...
5
votes
1answer
277 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 ...
8
votes
1answer
219 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 ...
7
votes
1answer
315 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 ...
0
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0answers
68 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 ...
8
votes
2answers
476 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 ...
1
vote
0answers
95 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 ...
3
votes
0answers
245 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 ...
1
vote
1answer
224 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 ...
2
votes
1answer
193 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 ...
5
votes
0answers
350 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 ...
3
votes
0answers
205 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 ...
4
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3answers
502 views

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

I know how to construction Koch snowflake ...
6
votes
1answer
148 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 ...
4
votes
1answer
320 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 ...
1
vote
1answer
95 views

FindProcessParameters for Fractional Brownian Motion Returns Error

I have the following data: ...
7
votes
1answer
533 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 ...
1
vote
1answer
178 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 ...
0
votes
1answer
237 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 ...
4
votes
1answer
340 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 ...
-4
votes
1answer
604 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 ...
2
votes
1answer
323 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 ...
3
votes
1answer
200 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 : ...
9
votes
2answers
468 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 ...
7
votes
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 ...
13
votes
2answers
628 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 ...
41
votes
9answers
8k 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 ...
4
votes
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. ...
24
votes
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)", ...
26
votes
5answers
4k 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. ...
47
votes
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 ...
11
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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 ...
47
votes
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 ...