Computation Model: Register Machine
All systems with computation model: register-machine
Systems (30)
Antikythera mechanism
f(x) = astronomical positions, eclipse prediction, Metonic calendar (multi-cycle gear ratios)
A hand-cranked bronze gearwork device built around 150–100 BC — the oldest known analog computer. Turning a single input crank advances 37 meshing gears whose tooth-count ratios encode the periods of ...
Coherent Ising machine (OPO network)
f(x) = Ising Hamiltonian ground state / combinatorial optimization (MAX-CUT, QUBO)
A network of degenerate optical parametric oscillator (DOPO) pulses circulating in a fiber ring cavity. Each pulse can oscillate in one of two phase states (0 or π), encoding a spin. Measurement-feedb...
Coupled oscillator network (Kuramoto / XY model)
f(x) = MAX-CUT / graph partitioning (approximate)
A network of identical oscillators — pendula, LC circuits, or CMOS ring oscillators — coupled to their neighbours by springs or resistive links. The Kuramoto model describes how each oscillator's phas...
Differential analyzer
f(x) = solutions to systems of ODEs (via chained mechanical integration)
Built by Vannevar Bush and Harold Hazen at MIT in 1928–1931, the differential analyzer is a general-purpose analog ODE solver. The core component is a wheel-and-disk integrator: a disk rotates at rate...
Diffractive deep neural network (D²NN)
f(x) = neural network inference / image classification (at the speed of light)
A stack of passive, 3D-printed diffraction layers implements a trained neural network entirely in the optical domain. Each layer is a mask with pixel-wise phase or amplitude modulation, trained offlin...
Hanging chain (catenary)
f(x) = hyperbolic cosine / thrust line
A chain suspended from two fixed points and left to hang under gravity settles into a curve that exactly realizes the hyperbolic cosine. Gaudí used physical catenaries (inverted) to design the arches ...
Kelvin tide-predicting machine
f(x) = sum of sinusoids / tidal height (Fourier synthesis)
Designed by Lord Kelvin (William Thomson) in 1872–73, this special-purpose mechanical analog computer performs real-time Fourier synthesis. Each tidal harmonic constituent (M2, S2, N2 …) is represente...
MEMS accelerometer
f(x) = Newton's second law (a = F/m) — continuous analog acceleration measurement
A microfabricated proof mass (typically silicon, ~1 μg) suspended by folded-beam springs. Under acceleration, the mass displaces by x = ma/k (Hooke's law + Newton's second law in equilibrium). Displac...
MONIAC (Phillips hydraulic computer)
f(x) = Keynesian macroeconomic equilibrium (ODE system)
Built by Bill Phillips (1949). Water flows through tanks and pipes representing economic sectors — income, consumption, taxation, investment. Flow rates encode economic quantities. The system settles ...
Marble computer
f(x) = binary arithmetic / boolean logic
Gravity-fed marble runs with rocker/seesaw gates implement binary arithmetic and logic operations. One marble = 1 bit. The rocker flips state on each pass, implementing half-adders and logic gates. Th...
Mechanical fire-control computer
f(x) = ballistic trajectory / gun bearing and elevation (multivariate real-time ODE)
Electromechanical analog computers installed on WWII-era warships (e.g. the US Navy Mark 1) continuously computed the correct bearing and elevation for naval guns from up to 25 live inputs: target ran...
Mechanical gyroscope
f(x) = time-integral of angular velocity (orientation tracking)
A spinning rotor mounted in gimbals conserves angular momentum. Any external torque causes precession perpendicular to both the spin axis and the applied torque — rather than tilting directly. By read...
Memristive Hopfield network optimizer
f(x) = optimization via chaotic annealing / transient dynamics
Memristive circuits implementing Hopfield network topology where the intrinsic nonlinearity of memristors creates transient chaotic annealing processes. The chaotic dynamics enable escape from local m...
Memristor crossbar
f(x) = analog matrix-vector multiplication
Crossbar arrays of memristors (memory resistors) perform matrix-vector operations in analog. Voltages applied to rows, currents collected from columns. Resistance values encode matrix elements. Enable...
Neuromorphic chip (Intel Loihi / IBM TrueNorth)
f(x) = spiking neural network computation
Silicon chips that mimic neural computation using spiking neurons and synaptic connections. Intel Loihi and IBM TrueNorth implement event-driven, asynchronous processing with on-chip learning capabili...
Op-amp analog computer
f(x) = ODE integration via Kirchhoff's laws
Operational amplifiers configured as integrators, adders, and multipliers solve differential equations in real-time. Voltages represent variables, circuit topology encodes the equation structure. Clas...
Optical correlator (4f / VanderLugt filter)
f(x) = cross-correlation / matched filtering (pattern detection in O(1) optical time)
A 4f lens system consists of two lenses separated by twice their focal length with a holographic or spatial-light-modulator (SLM) filter at the shared Fourier plane. The first lens computes the Fourie...
Photonic integrated circuit (silicon photonics)
f(x) = matrix-vector multiplication / unitary linear transforms (for neural network inference)
Arrays of Mach-Zehnder interferometers (MZIs) and microring resonators on a silicon chip implement programmable unitary matrices in the optical domain. Light encodes values as amplitude or phase; pass...
Planimeter
f(x) = area enclosed by an arbitrary plane curve (∮ via Green's theorem)
A two-bar linkage with a tracing point at one end and a measuring wheel mounted on the tracer arm. When the operator traces the boundary of an arbitrary shape, the wheel rolls only in the direction pe...
Reservoir computer
f(x) = temporal pattern recognition / dynamical system computation
Fixed nonlinear dynamical system (reservoir) coupled to a trained linear readout layer. Input drives the reservoir dynamics, output layer learns to extract desired computations. Echo state networks an...
Resistive sheet (Teledeltos) Laplace solver
f(x) = solutions to Laplace's equation ∇²φ = 0 (electrostatics, heat, groundwater flow)
A sheet of Teledeltos — carbon-coated resistive paper with ~6 kΩ/square resistivity — conducts current that obeys the same Laplace equation as electrostatic potential, steady-state heat conduction, in...
Rubber-band Steiner tree
f(x) = Euclidean Steiner minimum tree (approximate)
Elastic bands stretched between pins hammered into a board relax under tension to a state of minimum total length. Because each band pulls with a force proportional to its extension, the equilibrium c...
Simulated annealing (thermal)
f(x) = argmin of energy / cost landscape
A physical system coupled to a heat bath at slowly decreasing temperature explores its energy landscape. At high temperature it escapes local minima; as T→0 it settles into a global minimum — if cooli...
Slide rule
f(x) = logarithm, multiplication, division, roots
Logarithmic scales engraved on sliding rules allow multiplication by physical addition of lengths (log a + log b = log ab). Precision is bounded by engraving quality and human reading resolution — typ...
Soap film
f(x) = minimal surface (Plateau's problem)
A soap film spanning a closed wire boundary settles into the surface of minimum area — the solution to Plateau's problem. For two parallel rings it realizes a catenoid. Can approximate Steiner trees f...
Spaghetti sort
f(x) = total ordering of positive reals (sorting) in O(n) physical time
Cut n spaghetti strands to lengths proportional to the n values to be sorted. Gather them loosely in a fist and lower them vertically onto a flat table so all strands stand upright. Lower a flat hand ...
Thermodynamic computer
f(x) = sampling from Boltzmann distributions
Uses thermal noise in analog circuits to sample from Boltzmann distributions. Thermal fluctuations provide natural randomness that follows statistical mechanics principles. The Normal Computing SDE (S...
Thermodynamic computer (Normal Computing SPU)
f(x) = probabilistic sampling / linear algebra via thermal equilibration
Analog physics-based computers using thermodynamic principles for computation. Normal Computing's Stochastic Processing Unit (SPU) uses RLC circuits as unit cells with all-to-all coupling via switched...
Water (fluidic) computer
f(x) = binary addition / boolean logic (AND, XOR)
Water levels in vessels encode binary digits; a siphon and slow drain combine to implement AND and XOR in a single cup-and-tube unit. A filled cup is a 1, an empty cup a 0. When two cups feed one cont...
Watt centrifugal governor
f(x) = proportional speed regulation (continuous set-point tracking via negative feedback)
Two steel balls are mounted on hinged arms linked to a rotating vertical shaft driven by the engine. As engine speed increases, centrifugal force swings the balls outward and upward; through a collar ...