On [Wikipedia](http://en.wikipedia.org/wiki/Amoeba_%28mathematics%29) there some pictures of two dimensional amoebas (Thanks to [Oleg Alexandrov](http://en.wikipedia.org/wiki/User%3AOleg_Alexandrov/Pictures) for the pictures and the Matlab code he gives to build them). I was wondering if somewhere there are pictures of 3-dimensional amoebas. Should it look likes thick foam bubbles?



Picture of a 3 dimensional amoeba.
[There is now a 3-dimensional amoeba on wikipedia.](http://en.wikipedia.org/wiki/Amoeba_%28mathematics%29)


You are welcome. 
The main reason for the difficulty of making such amoebas is that it is the projection
of a 4-dimensional surface (the zero set of the polynomial). Finding a parametrization of the zeros set of an arbitrary polynomial in 2 variables is highly non-trivial.
The case on wikipedia is linear, thus we may easily parametrize it.
Now, this set is projected with $Log|\cdot|$, thus one has to be a bit careful which points to include to make the picture "pretty", since there may be zeros of the polynomial "far" away, and close to 0. 


I did not draw the projection of the parametrized 4-dimensional surface, but rather the projection of a lot of points on the surface, chosen in a manner that makes them somewhat evenly distributed.


EDIT: Also, rumour has it that Frank Sottile has some 3-dimensional amoebas somewhere on his [web page](http://www.math.tamu.edu/~sottile/index.html), but I have not been able to find them.


EDIT 2: Now, amoebas never look like soap bubbles, but the connected components of their complements do. (These components are always convex, aka. soap bubbles)


