Computer science

The registered systems of skcomplex.systems.computer_science. The page of each shows its factory, its component types with their states, parameters, and laws as written, and, for the forms that have them, its equations as SymbolicAnalysis returns them, so it serves as the pattern for a system of your own.

Automata

• Adding machine (odometer): The adding machine r → r + 1 on the q-adic integers, the odometer acting on the q-ary tree.
• Adleman DNA computation of a Hamiltonian path: Adleman's DNA computation of a Hamiltonian path, by random ligation of edge oligos in a test tube.
• Automata on the Grigorchuk group: The majority automaton on a ball of the Grigorchuk group, a group of intermediate growth.
• Automata on the free group: The majority automaton on a ball of the free group, a tree in which every cell follows its neighbours.
• Baumslag-Solitar groups: The majority automaton on a ball of the Baumslag-Solitar group BS(m, n), of exponential growth.
• Context-free subshift: A Markov chain on the context-free subshift, ternary rings where every block 0 1^h 2^k 0 has h = k.
• Diffusion automaton: A cellular automaton of diffusion, c' = c + r Σ (c_neighbour - c), started from a square of ones.
• Elementary automata: An elementary cellular automaton by its Wolfram number, started from a single live cell by default.
• Even and S-gap subshifts: The shift on the S-gap subshift, the binary sequences whose runs of zeros between ones lie in S.
• Fredkin's self-replicating parity automaton: Fredkin's parity automaton, whose local law copies any initial pattern into translated replicas.
• Game of Life: Conway's Game of Life, or another life-like rule, on a torus.
• Game of Life on a rewired small-world network: Conway's Game of Life on a small-world network rewired from the Moore lattice of a torus.
• Group-valued difference automaton: The automaton τ(x)(n) = x(n)^-1 x(n + 1) whose alphabet is a finite group, on a ring.
• Heisenberg: The majority automaton on a ball of the discrete Heisenberg group, of polynomial growth of degree 4.
• Highlife and the planar automaton zoo: HighLife, B36/S23, or any other life-like automaton of the planar zoo by its rule, on a torus.
• Involutive automaton: A binary automaton on a ring that is its own inverse, with the minimal memory set {-1, 0, ..., n}.
• Lamplighter: The parity automaton on a ball of the lamplighter group, a linear rule over the field of two elements.
• Langton's ant: Langton's ant, which wanders chaotically for about 10,000 steps before it builds a periodic highway.
• Lenia and its expanded universe: Lenia, a continuous automaton whose ring-kernel convolutions grow gliding, lifelike solitons.
• Life in a tree: The Game of Life on the free group F4, a tree of degree 8, surjective but not pre-injective.
• Linear automata over rings: The discrete Laplacian as a linear automaton on a ring, over the field of modulus elements.
• Morse subshift: The Thue-Morse substitution 0 → 01, 1 → 10, whose words make the language of the Morse subshift.
• Muller's pre-injective non-surjective automaton on F2: Muller's automaton on the free group F2, pre-injective but not surjective.
• Nilpotent automaton of class n: A binary automaton on a ring that is nilpotent of class n: n steps send every configuration to 0.
• Noisy automata: An elementary cellular automaton whose outputs are flipped at random with a small probability.
• Power-series automaton: The automaton τ(x)(n) = x(n) - t x(n + 1) over the ring K[[t]] of formal power series on a ring.
• Real quadratic automaton: The automaton τ(x)(n) = x(n + 1) - x(n)^2 over the reals on a ring.
• Self-indexed shift over a group alphabet: The map τ(x)(g) = x(g · x(g)) over the group as alphabet, continuous and equivariant but no automaton.
• Subshifts: A Markov chain on the golden mean shift, the configurations of a ring that never hold two adjacent ones.
• Subtraction automaton over the naturals: The automaton τ(x)(n) = max(0, x(n) - x(n + 1)) over the naturals, whose image is not closed.
• Surjective non-pre-injective linear automaton on F2: A linear automaton over K^2 on the free group F2, surjective but not pre-injective.
• Turing machine (three-state busy beaver): A Turing machine, a head with an internal state that reads, writes, and moves on a tape of symbols.
• Unbounded-alphabet automaton: An additive automaton over the nonnegative integers, x'(n) = x(n - 1) + x(n), from a single 1.

Evolutionary computation

• Bit-string evolution on a fitness landscape: A population of bit strings that evolves on a random additive fitness landscape.
• RobbyGA can collector and evolution by circumstance: Mitchell's genetic algorithm that evolves strategies for Robby, a robot that collects cans in a room.
• Simulated annealing, genetic algorithms, and differential evolution: A population of candidates that searches a two-dimensional landscape, one generation per step.

Neural networks

• Asymmetric diluted Hopfield network: The asymmetric diluted Hopfield network, which recalls a stored pattern below its memory capacity.
• Binary perceptron and random K-SAT: A binary perceptron that must store random patterns, revealed one per step, as cardinality constraints.
• Echo state network: An echo state network, a reservoir of leaky tanh units with random recurrent weights driven by a sine.
• Elman recurrent network trained by backpropagation: Elman's simple recurrent network, which learns to predict the next bit of a temporal XOR stream.
• Hopfield network: A Hopfield network that stores patterns with Hebb's rule and recalls the first from a corrupted copy.
• Next-generation reservoir computer: A next-generation reservoir computer whose variables follow the ridge readout of their monomials.