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I would like to draw a kind of diagram for mapping $\varphi:D\to D'$. Domains $D$ and $D'$ should look rather arbitrarily. I consider doing it with tikz but I do not know how to produce such nice curves for boundaries of domains.

enter image description here

After a while I got solution like this

\draw plot [smooth cycle] coordinates {(5,0.25) (6,0.35) (6.5, 0.2) (7,0.5) (7,1.65) (6.5,2.75) (5.8,2.75) (5.3,1.45) (4.8,0.85) } node at (6,1.7) {$D'$};
\path[->] (3.1,1.7) edge [bend left] node[above] {$\varphi$} (5.0,1.7);
\draw plot [smooth cycle] coordinates {(1.0,.1)(1.5,.2)(2.8,.5)(2.9,1.5)(2.8,2.8)(1.4,2.5)(0.5,0.5)} node at (1.8,1.7) {$D$};

enter image description here

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there are some blobby shapes at tex.stackexchange.com/questions/54985/amoeba-shape-with-tikz – David Carlisle May 11 '13 at 15:29
up vote 7 down vote accepted

Without TikZ. The shape is not exactly identical to your sketch above but I think it does not matter, doesn't it?

enter image description here

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