0
votes
1answer
67 views

Box counting fractal dimension

S: 1,0.3,0.22,0.12,0.06 N: 7,201,478,2595,17950 (no idea how to put this in a tally) I've got a question here where S is not shrunk by the same fraction throughout, I know how to work out the ...
6
votes
1answer
138 views

Definitions of Sierpinski Carpet and Higher Dimensional Analogues

We define the Cantor Set as: $Let \mathscr{J} := \{ 0, 2, \ldots , 3^{m-1} -1 \}$ for $m \in \mathbb{N}$, then $$C = [0,1] \setminus \bigcup_{m \in \mathbb{N}} \bigcup_{k \in \mathscr{J}} \Big( ...
0
votes
0answers
53 views

Cantor sets, Sierpinski carpets, and Menger sponge

How does one distiguish between iterations near infinity? Naturally there is an empty feeling about saying that the iterations $\forall k \in \mathbb{N} < \infty$, $\infty + k$ and $\infty - k$ are ...
0
votes
1answer
140 views

How to convert a right angled triangle into a equilateral triangle?

I want to use the Apophysis program to make a right angled sierpinski triangle into an equilateral triangle. But how can i do so? i have tried the second picture one but that is not correct.
1
vote
1answer
74 views

Describe attractors of a finite family of contraction mappings

The question is to describe the attractor of iterated function system $\mathcal{F}=\{R^2,f_1,f_2\},$ where $f_1,f_2$ are the two affine transformations$\begin{bmatrix} 0 & 0.8\\ -0.5&0 ...
2
votes
4answers
291 views

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 ...
2
votes
2answers
269 views

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 ...