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Questions tagged [fractals]

For questions on fractals, which are irregular, rough, or "fractured" sets that often possess self-similar structure.

The term fractal, derived from the Latin fractus meaning "broken" or "fractured," was coined by Benoît Mandelbrot in 1975 in order to describe mathematical objects (shapes, sets, processes, etc.) which possess irregular or rough structure at all scales. While there is little consensus on the precise definition of the term, fractals are typically characterized by self-similarity. The Cantor set, Sierpinski carpet, Koch Snowflake, and Mandlebrot set are examples of fractal sets.

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How would I go about generating this sort of fractal?

Don't really know if this question belongs here or on stack overflow, so sorry if this is not the right place. I have picture of this fractal: I have not seen this fractal among other more popular fractals. I don't know if this is a valid fractal.…
EIMA
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Fractal Analysis

Is there any way to compare two fractals and analyse the difference between the two. I'm doing a project on fractals and It'll be very easy if there is a module which can be used to analyse and compare fractals! Does such a thing exists?
Pranav Varma
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Is there a way to perform calculations of Mandelbrot set using only integer numbers?

I would like to create program in JavaScript (JS) which draws Mandelbrot set with arbitrary precision (zoom). In JS there is build in integer type BigInt which support simple operations like +,*,/,power on arbitrary precision integer numbers. JS not…
Kamil Kiełczewski
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Do all fractals have this property?

Fractals, when viewed as functions, are everywhere continuous and nowhere differentiable. Can this also be used as a definition for fractals? i.e. Are all fractals everywhere continuous and nowhere differentiable? And also: Are all functions that…
Truth-seek
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Can we have fractal dimension more than 3?

Menger sponge is a 3d fractal however it's fractal dimension is still less than 3. In fact most of the natural objects like coast lines have fractal dimensions between 2 and 3. This might be because we are calculating fractal surface dimension. But…
quantised
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What is the fractal dimension of a cauliflower?

I tried to calculate it's dimension using mass. Here's how I did, I took a small cauliflower and measured it's mass = 105g, then I divided it into 12 similar looking branches and calculated the mass of one of the branch (scaled down version) and got…
quantised
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Point on Mandelbrot set with copy of the original at a different scale

Today's featured picture on Wikipedia shows a deep zoom into a Mandelbrot set: http://upload.wikimedia.org/wikipedia/commons/a/a4/Mandelbrot_sequence_new.gif If one could pick any coordinate to zoom into, is there one which eventually takes one back…
Gnubie
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In Need of Ideas for a Small Fractal Program

I am a freshman in high school who needs a math related project, so I decided on the topic of fractals. Being an avid developer, I thought it would be awesome to write a Ruby program that can calculate a fractal. The only problem is that I am not…
fr00ty_l00ps
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Do 3 Dimensional Fractals exist?

I understand that certain mathematical sets produce fractals. Are there fractals defined by sets with more than 2 variables? Is that possible?
Alex
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Hausdorff's distance of some sets

We define $H^{n}$ for the set of all compact subsets of $\mathbb{R}^n$. Define the metric $\Delta$ in $H^{n}$ as following.Let $A,B \in H^{n}$ then define $d(x,B):= \min \lbrace d(x,y): y \in B \rbrace$ $d^{*}(A,B):=\max\lbrace d(x,B); x \in A…
Arsenaler
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Why does my carpet have so many holes?

I always liked the Sierpinski triangle, and happened upon the related article about the Sierpinski carpet. The article is pretty sparse, and states the area of the carpet is zero (in standard Lebesgue measure). Is there a proper proof or book in…
Muencher
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question about multifractal analysis

I have a general question about multifractal analysis: Suppose that I have two figures, that are multifractals. The question is, how I can compare how similar they are to each other? Can I do it by taking into consideration, that according to the…
Lila
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Is an Inverse Menger Sponge a fractal?

Is the Inverse of a Menger Sponge a fractal? I know a Menger sponge is fractal in nature, and it seems to me that the inverted form of it would be fractal as well, but I don't know.
aslum
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Julia Sets in Mathematica

stackexchange geniuses! I'm a high school student doing engineering research and am in need of some technical assistance. I'm working on a paper on using fractals in civil engineering and need to test which Julia Sets would be able to withstand the…
user3564
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Help with fractals

Let $f(z)=z^2+4z+1$. Is the filled Julia set (denoted $F_f$) connected? I'm not sure to show how its connected. The only thing I know how to do is verify whether a given point is in the set.
Chuck Franklin
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