I would like to produce a picture like this
How can I create the red arrows? I have managed to produce the large partitioned triangle and the smaller colored triangles : But I don't know of a good way to add the arrows. I would like them to be mostly parallel to the edges of the smaller triangles, and to bend smoothly at the corners.
Here is my code so far.
\documentclass[border=10mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=2]
\path
(0,0) coordinate (0)
(3,0) coordinate (1)
;
\path[rotate=60]
(3,0) coordinate (2)
;
\path
(0) -- (1) coordinate [midway] (01)
(1) -- (2) coordinate [midway] (12)
(0) -- (2) coordinate [midway] (02)
;
\draw[thick, fill=purple!50]
(0) -- (01) -- (02) -- cycle
;
\draw[thick, fill=red!50]
(1) -- (01) -- (02) -- cycle
;
\draw[thick, fill=orange!50]
(1) -- (12) -- (02) -- cycle
;
\draw[thick, fill=yellow!50]
(2) -- (12) -- (02) -- cycle
;
\draw
(0) node [below left] {$0$}
(1) node [below right] {$1$}
(2) node [above] {$2$}
%
(01) node [below] {$[0,1]$}
(12) node [above right] {$[1,2]$}
(02) node [above left] {$[0,2]$}
;
\end{tikzpicture}
\end{document}