Aleph::CA::TM_Gas_Rule Class Reference

Toffoli–Margolus (TM) lattice-gas block rule. More...

#include <tpl_ca_block_rule.H>

Public Member Functions
template<typename State >
constexpr Block_2x2< State >	operator() (const Block_2x2< State > &in) const noexcept
	Apply the TM lattice-gas block rule.

Detailed Description

Toffoli–Margolus (TM) lattice-gas block rule.

A close cousin of BBM that conserves particle count while exposing a different mobility pattern: particles bounce off horizontal walls instead of moving diagonally. For each 2×2 block:

• 1 or 3 alive → swap horizontally (NW ↔ NE, SW ↔ SE), modelling a horizontal-axis reflection.
• 2 alive on the same row → swap to the other row (vertical reflection).
• 2 alive on the same column → swap to the other column (horizontal reflection).
• 2 alive on a diagonal → swap to the other diagonal.
• 0 or 4 alive → unchanged.

Each branch is an involution and the resulting CA conserves the particle count exactly, making the Margolus update reversible bit-for-bit (forward(N) ∘ backward(N) = identity).

Definition at line 254 of file tpl_ca_block_rule.H.

Member Function Documentation

operator()()

template<typename State >

constexpr Block_2x2< State > Aleph::CA::TM_Gas_Rule::operator() ( const Block_2x2< State > &  in ) const

inlineconstexprnoexcept

Apply the TM lattice-gas block rule.

Template Parameters

State

binary cell state.

Parameters

[in]

in

current 2×2 block.

Returns

next 2×2 block.

Exceptions

This	function does not throw.

Definition at line 264 of file tpl_ca_block_rule.H.

References Aleph::and, Aleph::blossom_maximum_cardinality_matching(), and out.

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The documentation for this class was generated from the following file:

• tpl_ca_block_rule.H