0
votes
0answers
42 views

Basic concept books [closed]

I would like to refresh my basics & I would like to know the best books for the following topics [basic/beginner level with practical real life applications] Curves, Splines, Surfaces & ...
1
vote
0answers
16 views

Intersections of fractal sets with connected sets

Let $\beta \geq \alpha > 0$. Let $A\subset\mathbb R^n$ be a measurable set with Hausdorff dimension $\alpha$. Must there exist a closed connected set $B$ with Hausdorff dimension $\leq \beta$ ...
0
votes
1answer
104 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.
9
votes
3answers
317 views

Geometrical objects whose volumes are fractional powers of their sizes

While studying properties of foams (imagine bubbly soap or microscopical grids/networks), I started wondering on the relationship between the volume occupied by the matter $V_s$ itself and the overall ...
7
votes
0answers
190 views

Kakeya Needle problem video

I'm intruiged by the Kakeya Needle problem, described here on Wikipedia. Wikipedia has a nice animation of a needle turning through a hypo-cycloid: What I'm searching for is a visualisation of the ...
1
vote
3answers
178 views

Cantor Set and Fractals

I have read that the Cantor set is considered a fractal. I am referring to the Cantor set in which the middle third of a real line is removed recursively. I see that this is recursively defined, but ...
0
votes
0answers
73 views

Area fractal pentagrams III

how can I find the area of these two fractal? I've been try to solve some geometry exercises here but this and some other are so much difficult.
0
votes
0answers
111 views

Area fractal pentagrams II

A simple fractal. How to find the area of it? (only the arms of the star) Working with pentagrams is quite complicated, I can not solve this.
4
votes
3answers
335 views

Area fractal pentagrams I

When I saw this image I was a little curious. How can I find the area of this fractal?
3
votes
3answers
211 views

What's the analogue of Sierpinski triangle to disk?

What's the (closest) analogue of Sierpinski triangle to disk?
2
votes
1answer
71 views

About fractal structures

I read somewhere that we can not measure the length of the Adriatic Coast because it has fractal structure. I want some concrete explanation for the fractal structure
3
votes
1answer
147 views

Defining distance in fractal dimensions.

Is it possible define a distance measure in fractal dimensions? namely, what the generalization of $$ D(x,y)=\left(\sum_i(x_i-y_i)^2\right)^{\frac{1}{2}} $$ in fractal dimensions?
0
votes
1answer
85 views

Fractal walking: well defined case or not?

Please consider the following recursive diagram: diagram Each triangle is connected at the midpoint of a side to the corner of an inner triangle which is 1/4 times the size. The total line length of ...
3
votes
1answer
126 views

Snow Flake Problem: Limit of perimeter & area at $\infty$

I am supposed to find the limits as $n\rightarrow\infty$ of the perimeter & area of a snow flake. $$N_n = \text{Number of sides} = 3\cdot 4^n$$ $$L_n = \text{length of side} = \frac{1}{3^n}$$ ...
3
votes
1answer
79 views

understanding if a point is inside or outside a Koch fractal curve

I continue this post because i have a problem: understand if a point is inside or outside a Koch curve. I can find the third point of a equilateral triangle (and i need it for build a koch curve) but ...
8
votes
3answers
1k views

A way to determine the ideal number of maximum iterations for an arbitrary zoom level in a Mandelbrot fractal

I've created a JavaScript-based fractal drawer which you can see here: http://jsfiddle.net/xfF3f/12/ As you're probably all aware, a Mandelbrot Set is created by iterating over pixels as though they ...
4
votes
2answers
325 views

Is the number of circles in the Apollonian gasket countable?

Is it correct to say that the number of circles in an Apollonian gasket is countable becuase we can form a correspondence with a Cantor set, as their methods of construction are similar? What about ...