Dimensionality of spacetime

Showing the different possible and impossible spacetime dimensions.
Reproduction of Figure 1 in “On the dimensionality of spacetime” (1997) by M. Tegmark (arXiv:gr-qc/9702052).

Edit and compile if you like:

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% Author: Izaak Neutelings (June 2022)
% Inspiration:
%   "On the dimensionality of spacetime", Max Tegmark
%   https://arxiv.org/abs/gr-qc/9702052
\documentclass[border=3pt,tikz]{standalone}
\usepackage{siunitx}
\usepackage[outline]{contour} % glow around text
\contourlength{1.1pt}
\usetikzlibrary{3d} % for canvas
% STYLE
\tikzset{>=latex}
\tikzstyle{border}=[thick,blue!15!black]
\begin{document}
% DIMENSIONS
\begin{tikzpicture}[scale=1]
  \def\A{0.15}   % amplitude of sine wave cut off
  \def\xmax{5.5} % maximum dimension
  \def\sinecut{  % path of sine wave cutoff
    (\xmax,0) -| (0,\xmax) -- 
    plot (\x,{\xmax+\A*sin(deg(2*pi*\x)))}) -- (\xmax,\xmax) --
    plot ({\xmax+\A*sin(deg(2*pi*\x)))},\xmax-\x) -- cycle
  }
  
  % CHART
  \colorlet{col-elliptic}{magenta!90!red!95}
  \colorlet{col-unstable}{cyan!90!black}
  \colorlet{col-simplist}{red!75!black!90}
  \colorlet{col-tachyons}{yellow}
  \colorlet{col-unpredic}{green!45!black!80}
  \colorlet{col-werehere}{white}
  \begin{scope}
    \clip[samples=200,domain=0:\xmax] \sinecut;
    \fill[col-elliptic] (0,0) rectangle (6,6); % elliptic
    \fill[col-unstable] (1,1) rectangle++ (6,6); % unstable
    \fill[col-simplist] (1,1) rectangle (3,3); % too simple
    \fill[col-werehere] (3,1) rectangle++ (1,1); % we are here
    \fill[col-tachyons] (1,3) rectangle++ (1,1); % tachyons
 
 
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