Whereas the Cell Matrix is built around the idea of Boolean truth tables, the Songline Processor enables one to design systems using real-valued building blocks. This means that instead of a Boolean-valued truth table, each cell contains something like n real-valued function of n variables for mapping n inputs to n outputs. Cells are connected to nearest neighbors as with the Cell Matrix, and inputs are continually evaluated to produce outputs, which are evaluated by neighbors as their inputs, and so on.
The motivation for this is simple: the natural world appears to be more analog than digital, meaning that most of the things we observe and manipulate are better represented as real values vs. binary states. Of course a collection of binary states can be used to approximate a real value (simply by digitizing a real number), and in fact this is how the current simulator operates; yet it's potentially interesting to consider a system that operates with real-valued functions as part of its inherent, low-level architecture. This is one goal of the SLP.
Analog C/D Mode
In the Cell Matrix, each cell operates in one of two modes: C or D mode. This is, again, a binary notion. The SLP extends this to more of an analog notion, by allowing each cell to be in both C and D mode, to different degrees, based on the the cell's real-valued C inputs. Thus a C input of 0 causes a cell to operate in pure D mode, whereas (say) a C input of 1 might represent pure C mode. An input of 0.5 would thus place the cell in equal-parts C and D mode.
Recall the setup for the Cell Matrix: in D mode, the cell uses inputs to select a row from its truth table, whereas in C mode the inputs are used to repopulate the rows of the truth table. In a fractional mode, the SLP does both: “truth table bits” (the way the cell maps inputs to outputs) become a mix of their present value and the incoming signal, with the mix specified by the C input. Output values are a mix of the cell's function's value at the given input point, and the function itself (again, the equivalent of the truth table bits in the digital Cell Matrix).