We present Cyclotron, a compiler that expresses streaming dataflow algorithms using recurrence equations, which are then compiled to distributed topologies of interlinked processors. Our compiler lowers a language of recurrences over logical iteration spaces into per-processor programs of sends, receives, and computations. In these recurrences, data accesses are not limited to external accesses to memory; data can live separately on the iteration space itself, allowing internal points to communicate values directly with other points. Users specify this communication directly in the recurrence language, which allows them to express various communication patterns such as a nearest-neighbor systolic exchange, a one-to-all broadcast, a bidirectional split ring, or an asymmetric and piecewise broadcast pattern, which are often not supported by standard distributed linear algebra libraries. These recurrences describe the algorithm and communication independently of how they map onto the hardware. A programmer then chooses which dimensions execute across processors and which execute over time, without rewriting the entire program. Users only specify data dependencies across the iteration space, and the compiler safely generates a program, per process, with correct placement of both communication and computational operators according to the chosen space--time mapping. We evaluate distributed matrix multiplication, TRSM, Cholesky, and fused Cholesky--TRSM on up to 16 CPU nodes and 16 GPUs, comparing against ScaLAPACK, SLATE, and cuSolverMp. Cyclotron is competitive with and often outperforms these hand-optimized libraries; for Cholesky, the best communication strategy changes with problem size and architecture.

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