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Our long term goal is to execute General Purpose computation on homogeneouscomputing media consisting of millions of small identical Processing Elements(PE) communicating locally. We proceed by simulating the Self-Development of aNetwork (SDN) of membranes, and this implies a medium able to implementartificial physics laws that simulates simplified membrane-agents, dividing andhomogenizing. This is a difficult challenge: our current version of SDN-mediauses PEs with 77 bits of state and 13878 gates. This high level of complexityforced us to work out an efficient and expressive scheme for programming themedium, the goal of this paper it to present it. The PE's communication graphhas to be a maximal planar graph. Fields of bits are spread in 2D, over threelocus: the vertices, edges and faces of this planar graph. They constitutethree data types, which abstract away the ensemble of PEs. The simplicialproximity between bits is used to define operations on fields, thusimplementing "{\it spatial type}". Expression combining operations can betranslated in logical circuits.  The efficiency is achieved because fields of different locus are combinedusing reduction operation. This allows to factorize computation by exploitingthe symmetries always present when simulating physics.  The expressiveness is achieved by allowing a modular procedural programming:Instead of directly focusing on a specific target update function, we develop alibrary or reusable functions mapping fields to other fields.  We consider two kinds of maximal planar graph: with isotropic distribution ofPEs or with the hexagonal lattice structure. The first compares to amorphouscomputing medium and has a better potential for hardware scalability, thesecond compares with cellular automata computing medium, it is more efficient.

Modular programming of computing media using spatial types, for artificial physics