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The current trend in electronics is to integrate more and more transistors on a chip and produce massive hardware resources. As a consequence, traditional computing models, which mainly compute in the temporal domain, do not work well anymore since it becomes increasingly difficult to orchestrate these massive-scale hardware resources in a centralized way. Spatial computing is a unifying term that embodies many unconventional computing models and means computing on a relatively homogeneous physical medium made of hardware components, where the communication time is dependent on the Euclidean distance between the components (locality constraint). This constraint makes the programming for high performance significantly more complex compared to classical non-spatial hardware because performance now depends on where computation happens in space (mapping problem). Blob computing is a new approach that addresses this parallel computing challenge in a radically new and unconventional way: it decouples the mapping of computations onto the hardware from the software programming while still elegantly exploiting the space of the underlying hardware. Hardware mapping of computations is done by a physical force-based approach that simulates forces between threads of computation (automata). Attractive forces are used to keep automata that need to communicate with each other closer while repulsive forces are used for load balancing. The advantage of these primitives is that they are simple enough to be implemented on an arbitrary computing medium. They form the basis of a runtime system (RTS) that transforms an arbitrary computing medium into an easier-toprogram virtual machine called the blob machine. The basic objects of the blob machine are those automata, and the instructions let automata create new automata in specific ways so as to maintain a hierarchical organization (which facilitates both the mapping and the programming). We detail the basic instructions of the blob machine and demonstrate their confluence. Programming a spatial medium to perform a given algorithm then boils down to programming the blob machine, provided the RTS is implemented on it. The advantage of this approach is the hardware independency, meaning that the same program can be used on different media. By means of several examples programmed using a high-level language description, we further show that we can efficiently implement most current parallel computing models, such as Single Instruction Multiple Data (SIMD), data parallelism, "divide-and-conquer" parallelism and pipelining which demonstrates parallel expressiveness. On sorting and matrix multiplication algorithms, we also show that our approach scales up optimally with the number of basic hardware components.

When programming a spatial computing medium such as a cellular automaton, the hop count distance to some set of sources (particles) is an often used information. In particular, we consider the case where the sources themselves are moving. Due to the locality of communication, only an estimation of the distance can be made at each time step, and each location. When no assumption is made on the size of the medium, that distance takes its values in N, which is not desirable, because it does not lead to finite state. This paper shows how to use the modulo operation to project that set of N-fields into a finite set of Z/nZfields. Using the modulo stored at each site, we show that we are still able to compute the local differential of the original field, allowing to manipulate the former as a directional gradient. It allows us to evaluate the direction of the nearest source, provided the sources move at bounded speed, less than one site per time unit. This information can be used to solve several problems of spatial nature. In the particular case of cellular automata, we present two rules using the modulo representation of distance field: Voronoi Diagram and Convex Hull. The two rules applies for moving sources, although at the moment, the convex hull has been implemented only for static sources.