Mathematics Stack Exchange
Mathematics Stack Exchange

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.

1220 questions
0
votes
0 answers

What is the name of this fractal?

I can't find the official name of this in my textbook. Can anyone help me out?
CuriousJ
  • 87
  • 1
  • 1
  • 3
0
votes
1 answer

Information on this fractal?

I was bored and started thinking of fractals and decided I scribbled what I thought could be one. $$a_{i+1} = (a_i - b_i) / c_i $$ $$b_{i+1} = (b_i - c_i) / a_i $$ $$c_{i+1} = (c_i - a_i) / b_i $$ I was just wondering if there was any information on…
Tolure
  • 217
0
votes
1 answer

Definition of Area of a Two Dimensional Line

I learned recently that lines such as the boundary of some Julia sets and the Hilbert curve have area. I was wondering what the strict definition of such an area would be, and I intuitively came up with the following: Let $S$ be the set of all…
William Grannis
  • 1,844
0
votes
1 answer

Triangular subsets of the Sierpinski triangle

Consider the Sierpinski triangle. We can easily find three points and three segments of it to form a regular triangle, which is a triangular subset of the Sierpinski triangle. Question: What is the cardinality of all triangular subsets of the…
user561154
0
votes
1 answer

Fractals - exact and self similarity

Can someone explain me what is the difference between strictly and exactly self-similar fractals? What is the stronger possession and what are the examples for both types? Thanks in advance.
user121
  • 527
0
votes
1 answer

Mandelbrot precision target the center of a pixel?

I read this question and I don't understand the answer: https://stackoverflow.com/questions/8381675/how-to-perform-simple-zoom-into-mandelbrot-set?rq=1. Especially how can I aim for the center of the pixel like so: for(unsigned SX = SMin; x <…
Micromega
  • 115
0
votes
2 answers

Fractals and measuring a piece of paper

Traditionally, I was taught that a piece of paper was 2d, so I decided to measure it, as if it was a square, since for a square, the area is just the length of one side squared. So for an 8.5 by 11 inch sheet of paper, the area would be 93.5 in^2.…
user463013
  • 57
0
votes
1 answer

How to iteratively construct a fractal with dimension d = ln(a)/ ln(b)?

I know that if the dimension of a fractal is $\ln(a)/\ln(b)$ then $a$ is the number of copies needed to construct a larger version of it, and $b$ is the magnification factor. However I'm not sure where to go from here.
mathstack
  • 899
0
votes
1 answer

Fractal dimension of a polygonal line.

Given an ordered set of points in the unit square, what are the most elegant ways to estimate the fractal dimension of the curve? By "elegant" I mean without resorting to drawing the object and doing box counting...
user408878
  • 3
  • 2
0
votes
0 answers

Fractal dimension of a set of points in $\mathbb{R}^2$

I have a set of points in $\mathbb{R}^2$, of the form: $\left(\frac{a}{\ell^2},\frac{b}{\ell^3}\right)$ where $\ell>0$ is an integer and $a$ and $b$ are some real positive numbers. I am interested to know the fractal dimension of this set of points…
user12588
  • 399
0
votes
5 answers

what is $c$ in Mandelbrot set?

The Mandelbrot Set is an extremly complex object that shows new structure at all magnifications. It is the set of complex numbers $c$ for which the iteration indicated nearby remains bounded. $$z_0=c$$ $$z_{n+1}=z_n^2+c$$ what is $c$ in Mandelbrot…
Salvador
  • 13
0
votes
0 answers

What´s the dimension of a Sierpinski fractal?

I know the dimension of a Koch snowflake (log4/log3), but what numbers do I have to put in to obtain the dimension of a Sierpinski fractal?
Deschele Schilder
  • 1
  • 1
  • 8
0
votes
1 answer

Infinite number of points in the Sierpinski Triangle

I have basic background in mathematics (Linear Algebra, Calculus) and I've been reading up on fractals, because I find them fascinating. I can't understand one thing in basically all of the fractals created using the iterated function systems. For…
studen
  • 221
0
votes
1 answer

Understanding the expression of fractal dimension in plants

I just finished a small, demo exercise on fractal dimension of a plant by using MATLAB and box-count method. There were two different treatments. A plant treated with a specific hormone and a plant without treated with anything. Above there are the…
F.N
  • 125
-1
votes
1 answer

Newton fractal formula conversion to coordinate plain

starting to do some shader with Newton fractal I can't understand examples. If I have $$z^{2}+c$$ fractal, it could be presented as a $$(a +b*i)^{2}+c$$ $$a^{2}+2*a*b*i - b^{2}$$ and I will get point with coordinates $$vec2(a^{2} - b^{2},…
An Anita
  • 1
1 2 3
…
11
12