Questions tagged [visualization]

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11 votes
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Visualization and new geometry in higher stacks

I am trying to develop a geometrical intuition for "higher spaces", i.e. both in the sense of higher dimensional spaces (more than three dimensions) and in the sense of abstractions beyond ...
Martin Hurtado's user avatar
8 votes
0 answers
422 views

What is the nicest bijection $\textbf{R}^p \to \textbf{R}^q$ that you know?

It is well-known that bijection between $\textbf{R}^p$ and $\textbf{R}$ exist (e.g. here, though many other examples exist). The problem with all these examples of bijections is that typically the ...
8 votes
0 answers
1k views

Visualization of an algebraic stack

As the visuallization of an algebraic stack is virtually impossible I warn about this is a soft question. I am interested in thinking visually about algebraic stacks (also higher and derived stacks, ...
Martin Hurtado's user avatar
3 votes
0 answers
232 views

Visualization of hidden structures in numbers

[Please allow me a note: The way desribed below allows to depict functions $f:X^2 \rightarrow Y$ completely in two dimensions (without hiding or omitting any information). This allows for depicting ...
Hans-Peter Stricker's user avatar
2 votes
0 answers
126 views

Visualisation of general 3x3 matrices, with applications to the pedagogy of linear algebra?

I've got a method for visualising non-zero $2 \times 2$ real matrices (modulo non-zero scalar factor) using the fact that: Nonnegative determinant matrices (modulo non-zero scalar factor) are in 1-to-...
wlad's user avatar
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1 vote
0 answers
367 views

Astonishing affinity of Wolfram's rule 110 to the numbers 2 and 7

I investigated the evolution of a single black cell on 1-dimensional grids with periodic boundary conditions of variable sizes $N$ under Wolfram's rule 110 which is the only one for which Turing ...
Hans-Peter Stricker's user avatar
1 vote
0 answers
45 views

Barycentric coordinates of weighted edges

Given $K_n$ with weighted edges, we can fix an edge $e_{AB}$, iterate over all non-adjacent edges $e_{CD}\in E\setminus e_{AD}$ and record how often $e_{AB}$ was in the lightest, intermediate or ...
Manfred Weis's user avatar
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1 vote
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42 views

Methods for useful visualisations of complete weighted graphs

Question: which methods for visualising complete weighted and symmetric graphs, i.e. $K_n$, are useful in the sense that they can aid in mathematical research? The Traveling Salesman Problem may ...
Manfred Weis's user avatar
  • 12.6k
1 vote
0 answers
165 views

Imagining linear maps between finite fields

I can't imagine a right picture of a linear transformation $\mathbb{F}_{p} \mapsto \mathbb{F}_p$ or $\mathbb{F}_{p^2} \rightarrow \mathbb{F}_{p^2}$ etc (over the field $\mathbb{F}_p$) although they ...
katana_0's user avatar
  • 353
1 vote
0 answers
57 views

Open volumetric time series data set

Does anyone know where I can find a good open volumetric time series data set? I had a look at some of Stanford's open data sets (https://graphics.stanford.edu/data/voldata/ ) But these do not seem ...
sav's user avatar
  • 191
1 vote
0 answers
221 views

What is the state of the art of visualizing bifurcations for "difficult" dynamical systems?

This question is related to my other recent question on MO (although I am not confident that the dynamical system described in that other question is actually "difficult," in the sense that I will ...
Aaron Golden's user avatar
0 votes
0 answers
98 views

Possible shifts in finite elementary cellular automata

I investigated the long term behaviour of a pair of black cells ■■ on a circle of $N$ cells under the action of each of Wolfram's rules $R$. For each combination $(R,N)$ I determined the first ...
Hans-Peter Stricker's user avatar
-2 votes
0 answers
151 views

Visualizing shapes of initial segments of $\mathbb Q$?

A posted answer to this earlier question of mine caused me to think that I had not asked the particular question that I actually wondered about, so that will appear here. A nonempty proper initial ...
Michael Hardy's user avatar