**9**

votes

**0**answers

139 views

### Decay rate of measures on Cantor set

I've read that Kahane and Salem show that if $\mu$ is any measure supported on the ternary Cantor set, then $\hat{\mu}(\xi) \not\to 0$ as $|\xi| \to \infty$, however I have been unable to find a ...

**4**

votes

**0**answers

533 views

### What is known about the area of the symmetric Pythagorean tree?

What is known about the area of the symmetric Pythagorean tree? (Closed unit square as base, area of enclosed triangles not included.) The problem in calculating the area is that squares start to ...

**3**

votes

**0**answers

99 views

### Possible Hausdorff dimension of intersection of Besicovitch-Eggleston like sets

Let $b \geq 2$ be an integer and suppose that $v=(p_0,\cdots,p_{b-1})$ be a probability vector. Let $S_{b,v}$ be the set of real numbers whose $b$-ary expansion has the digit $k$ with relative ...

**3**

votes

**0**answers

237 views

### Picture of the set of discontinuity of degree 2 rational Julia sets

Let $Rat_d$ be the set of all rational fraction of degree $d$ and $X_d \subset Rat_d$ be the bifurcation locus of rational fractions of degree $d$, i.e. the closure of the set of discontinuity of the ...

**2**

votes

**0**answers

153 views

### A fractal object at origin but nowhere else: derived from Brownain motion

Hi,
Please consider this object: Start with a realization of Brownian motion in 2D, which I'll denote by rho(t) where -infinity < t < +infinity. Next, lets smooth rho. There are various ...

**2**

votes

**0**answers

474 views

### Self-similarity of Riemann's “non-differentiable” function

I hope it doesn't seem inappropriate for me to raise on MO an unanswered question from MSE, indeed a question actually posed there by someone other than myself.
I want to ask the following:
1) ...

**2**

votes

**0**answers

247 views

### Complexity of a variant of the Mandelbrot set decision problem?

This is a modified version of a question posted on StackExchange TCS.
Mandelbrot set is defined using the complex equation $P_c (z)=z^2 +c$ where $c$ is a complex number. Let us define
...

**1**

vote

**0**answers

188 views

### Classification of Self similar sets

I am looking at self similar sets in $\mathbb{C}$ defined as the fixed set or a sequence of contractions or an iterated function system. I am currently trying to classify these sets by how they are ...

**0**

votes

**0**answers

52 views

### Koch snowflake construction in many dimensions

I'm looking for some references to deal with the Koch snowflake construction. The construction basically says we can find a sequence $E_k$ such that $\sup_k|E_k|<\infty$ but $P(E_k) \rightarrow ...

**0**

votes

**0**answers

43 views

### Fractal in discrete time series/discrete time sequence

Consider a time series of real number $x_1, x_2,\dots,...x_n$. How one can define fractal dimension of this series?
I would like to know famous formula $F+H=2$ where H is Hurst exponent and F is ...