bio  website  math.uvic.ca/faculty/aquas 

location  University of Victoria  
age  46  
visits  member for  3 years, 9 months 
seen  6 hours ago  
stats  profile views  3,481 
The pic is the phase portrait of a simple "piecewise isometry". Define a map by sliding the two halves of the plane: the top half to the right; the lower half to the left and then rotate. Around each periodic point of the map there's a "periodic island". These are what are in the image...
7h

comment 
Aperiodic set of corner Wang Tile
If you believe the answer to your previous question mathoverflow.net/questions/164400/… which you accepted, then an aperiodic edgetype Wang tile translates directly to an aperiodic cornertype Wang tile. 
23h

comment 
Digits <> Numbers
If you decide to ask on MSE, make sure to explain what you've managed to do already. People there don't like being asked to do your homework unless you explain that you've done something yourself. 
2d

comment 
boundary density of the Von Koch flake
Right. Presumably the $\infty$ is a typo. All points have the same limit in the $\infty$ direction. 
Aug 18 
comment 
Integer valued polynomial through some points with rational coordinates
If you're looking for an integervalued polynomial such that $y_i=P(x_i)$ for each $i$, you should certainly assume the $x_i$ are distinct(!) 
Aug 17 
comment 
Linear dependency of real numbers with integer coefficients adding up to zero
Your question is precisely whether the reals $x_2x_1$,...,$x_nx_1$ are linearly independent over the rationals. 
Aug 12 
answered  Bounded martingales of infinite path length 
Aug 12 
awarded  Popular Question 
Aug 5 
comment 
Name of a generalized version of semicontinuity
The empty set is open. Do you mean $f^{1}U$ contains a nonempty open set whenever $U$ is a nonempty open set? 
Jul 31 
comment 
Is any particular algebraic number known to have unbounded continued fraction coefficients?
Nice revision @StevenStadnicki! I didn't understand at all what the original question was asking. 
Jul 30 
comment 
Prove that …, f(x2), f(x1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
Instead of changing the norm, I think it's probably nicer to say you know the space of translates is finitedimensional, so pick a (finite) orthogonal basis. By the condition in this answer, the inner product with any basis element goes to 0. Hence the strong norm (of $f(xk)$) goes to 0 as $k\to\infty$. 
Jul 28 
comment 
Double Markovity
Do you mean that you have three random variables $X$,$Y$ and $W$ all defined on the same probability space, such that $\mathbb P(Y=yX=x,W=w)=\mathbb P(Y=yW=w)$ and $\mathbb P(W=wX=x,Y=y)=\mathbb P(W=wY=y)$? 
Jul 26 
comment 
Pairwise dependent random walk recurrent
Your summands have the property of 1dependence: if $ij>1$, then $X_i$ and $X_j$ are independent. There are CLT for 1dependent random variables. The events that $\limsup S_n=\infty$ and $\liminf S_n=\infty$ are tail events, and therefore have probability 0 or 1 by Kolmogorov's 01 law. It's not hard to see the probability is not 0. 
Jul 25 
comment 
The lonely molecule
If they're randomly placed, then they will almost surely cluster somewhere sooner or later. It's easiest to work on the torus, but completely equivalent because you can unfold $2^d$ copies of the cube to make 1 copy of the torus. 
Jul 19 
comment 
A nonstandard ergodic limit
I don't think it's right that the answer is yes for an irrational rotation and the function $f$ is taken to be $L^1$. There is a theorem called the transference principle (I think of it as a photocopying machine) allowing you to transfer a counterexample that diverges for one measurepreserving transformation to any other aperiodic measurepreserving transformation. 
Jul 17 
comment 
Lebesgue measure of a set of irrational numbers
I don't think @EmilJeřábek is right here. The fact that the geometric mean of the $a_i$'s is something doesn't tell you how big the largest one is. 
Jul 8 
comment 
Volume of normal cone of a simplex (at a vertex)
Right. The cones $C_j=\{y\colon y_j=max_{i=1}^n y_i\}$ have the same volume: the orthogonal transformation that simply rotates the string of coordinates by one place: $(y_1,\ldots,y_n)\mapsto (y_n,y_1,\ldots,y_{n1})$ maps $C_j$ to $C_{j+1}$. 
Jul 8 
comment 
Is the universal constant in Caccioppoli's inequality one?
Why is $\nabla(u\chi)\le u\nabla\chi$? 
Jul 7 
awarded  Nice Answer 
Jul 7 
revised 
Volume of normal cone of a simplex (at a vertex)
added 4 characters in body 
Jul 7 
comment 
Base change for $\sqrt{2}.$
Algebraic irrationality "is independent of" base expansions; there are countably many algebraic irrationals; Therefore "with probability 1", all algebraic irrationals are normal to all bases. 