Because the Cambrian explosion generated the largest of organic life's complexity increases, it is interesting to consider what its digital analogue may be. At its most fundamental level, the Cambrian explosion arose out of the transition from single to multi-cellular organisms. The digital analog would be a transition from serial to parallel processes.
If we make an analogy between the cell and the processor, then modern multi-cellular organisms are parallel programs on a scale of complexity that vastly exceeds any existing computer software. In organic life, the program is the genome, based on nucleic acid sequences. In humans this program has roughly three billion bases, expressed as roughly one hundred thousand genes. However, no individual cell expresses all the genes in the genome. Each cell expresses a small subset of the genes, and this subset defines which ``cell type'' the cell is. It may be a skin cell, liver cell, brain cell, etc. depending on what subset of genes it expresses.
The human body is thought to have several hundred distinct cell types, with a total of trillions of cells. This corresponds to the two main types of parallelism in computer software: SIMD and MIMD. In SIMD parallelism there is a single instruction pointer shared by all of the processors, so every CPU executes the same code in synchrony. In MIMD parallelism, each CPU has its own instruction pointer, so each processor is capable of executing a different set of code.
SIMD parallelism corresponds roughly to multiple cells of a single cell type, in that in both cases, the same genetic code is being expressed. MIMD parallelism corresponds to multiple cells of different cell types in that different cells are expressing different code. Large modern multi-cellular organisms combine both SIMD and MIMD parallelism on a massive scale.