Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0103057

Finding The Sign Of A Function Value By Binary Cellular Automaton

H. F. Chau·H. Xu·K. M. Lee·L. W. Siu·K. K. Yan
View original source ↗Read source document ↗Export metadata ↓

Abstract

Given a continuous function $f(x)$, suppose that the sign of $f$ only has finitely many discontinuous points in the interval $[0,1]$. We show how to use a sequence of one dimensional deterministic binary cellular automata to determine the sign of $f(ρ)$ where $ρ$ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that $f$ satisfies certain technical conditions.

Explore related subjects

nlin.CGcond-matcs.CC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

H. F. Chau, H. Xu, K. M. Lee, L. W. Siu, K. K. Yan. 2001-03-30. Finding The Sign Of A Function Value By Binary Cellular Automaton. https://doi.org/10.1142/s0129183102003929

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Dimension-dependent continuum limits in tissue mechanics

Continuum descriptions of epithelial tissue mechanics can replace expensive individual-based simulations with tractable macroscopic models, yet the link between cell-scale forces and tissue-scale transport remains poorly understood. We show that dimensionality controls this link: long-time mechanical relaxation rates reveal generalized porous-media-type nonlinear transport phenomena, $D(ρ)\proptoρ^γ$. Exponents in nonlinear diffusivities are fixed by microscopic mechanics and dimensionality, providing a novel physical mechanism for emergent macroscopic transport phenomena.

nlin.CG↗
arXiv2026

Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre

The hat and spectre monotiles, discovered in 2023, tile the plane only aperiodically; no cellular automaton dynamics on these tilings has previously been reported. Cellular automata are studied here on patches generated by finite-state transducers, so that every experiment regenerates deterministically from a small record. Within edge-adjacency semi-totalistic rules, exhaustive and evolutionary searches find only mortal travelers: gliders are absent. Guided by a reproduction of the known Penrose-tiling glider, the rule space is extended to vertex neighborhoods and to priority-table rules whose non-quiescent states are visible to neighbors. Evolutionary search then discovers gliders on both monotilings; tracked by a sliding window that regenerates the patch along the flight, they travel one million rings at constant speed and heading. All headings are quantized, to millidegrees, onto a six-spoke compass - the fast axes of the tiling's graph metric. An ablation shows both rule-space extensions are individually necessary. All results replay exactly in an accompanying interactive essay.

nlin.CG↗
arXiv2026

Game of Life on Archimedean Lattices: Glider Guns and Phase Dynamics

I explore Conway's Game of Life (GoL) on six composite Archimedean lattices. On the Kagome lattice, on which small gliders and puffers appear particularly frequently across inputs, I use the output of a symmetry-constrained evolutionary search algorithm to construct a novel glider gun. The glider gun comprises four interacting bouncers and stably emits a small glider every 276th generation. Serving as an extension of classical GoL, I also propose cells with a phase degree of freedom and an associated local phase rule, which on the Kagome lattice is demonstrated to host phase-periodic gliders. This enables the possibility of phase-sensitive and interference-based computations.

nlin.CG↗