hris, here is a very simple code, in which the dynamics of the particles are governed by viscous drag alone. The bonds are all linear springs, and those at the edge of the figure (in black) have one hundred times the spring constant of those in the middle (in red). You can control the simulation with the following keys:

    a, s, w and z to move the shape around the screen

    1 and 3 to make the number of generations larger and smaller.

    2 to reset the positions

    4 to toggle between regular and Sierpinski geometry (this is the interestin one!)

    t,y,u,i,o,p to change the force

The force is shown at the top of the screen, and acts centrally on the outermost three particles. I have also calculated a maximum offset due to buckling of the particles along one edge, compared to the two corners. If the outside bonds were infinitely stiff (so they would be rigid but freely hinged rods), then this offset would be strictly zero up to the point that buckling first occurs. However, the finite stiffness of the outer springs, together with small random forces that are applied to the particles (to break any lingering symmetry), mean that this offset is always slightly non-zero for any geometry other than the lowest generation, and grows smoothly as the compressive force increases.

I think that the next steps are to strictly linearize this problem, so that it can be simulated with strictly incompressible outer bonds. This I believe will be the limiting case for a real structure under light loading (i.e. the optimum distribution of mass between inner and outer bonds will be strongly in favour of outer bonds). The linearized problem can then be solved by a combination of dynamics for the outer particles (probably including inertia, just like a molecular dynamics simulation), and solving for the positions of the inner particles using a conjugate gradients minimization. Anyway, all that is for the future, and I'll put it in a new simulation when I have the chance to do some more coding.