ca_voter_model_example.cc

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
#include <array>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <random>
#include <sstream>
#include <string>
#include <vector>
 
#include <tpl_ca_graph_automaton.H>
 
using namespace Aleph;
using namespace Aleph::CA;
 
namespace {
 
// Voter rule with a unique sub-seed per call — deterministic given
// the engine schedule (which itself is deterministic).
class Voter_Rule
{
  std::uint64_t seed_;
  mutable std::uint64_t calls_ = 0;
 
public:
  explicit Voter_Rule(std::uint64_t seed) noexcept : seed_(seed) {}
 
  [[nodiscard]] int operator()(int current, Neighbor_View<int> neigh) const noexcept
  {
    if (neigh.empty())
      return current;
    std::uint64_t key = seed_;
    key = (key * 1099511628211ull) ^ (calls_ + 1);
    ++calls_;
    std::mt19937_64 rng(key);
    std::uniform_int_distribution<std::size_t> pick(0, neigh.size() - 1);
    return neigh[pick(rng)];
  }
};
 
// Build a "bowtie": three triangles glued at node 0.
Array<Array<std::size_t>> build_bowtie()
{
  // Nodes: 0 (hub), then three triangles {1,2}, {3,4}, {5,6}, each
  // forming a triangle with node 0.
  Array<Array<std::size_t>> adj(7, Array<std::size_t>{});
  auto edge = [&](std::size_t a, std::size_t b)
  {
    adj[a].append(b);
    adj[b].append(a);
  };
  // Triangle 1
  edge(0, 1); edge(0, 2); edge(1, 2);
  // Triangle 2
  edge(0, 3); edge(0, 4); edge(3, 4);
  // Triangle 3
  edge(0, 5); edge(0, 6); edge(5, 6);
  return adj;
}
 
void print_state(const Graph_Lattice<int> &lat, std::size_t step)
{
  std::printf("Step %4zu :", step);
  for (std::size_t n = 0; n < lat.size(); ++n)
    std::printf(" %d", lat.at_node(n));
  std::putchar('\n');
}
 
std::string render_tikz(const Graph_Lattice<int> &lat)
{
  // Hard-coded layout: the hub at (0,0), the three triangles around
  // it at 120-degree increments.
  std::ostringstream os;
  os << "% Aleph::CA voter model bowtie\n";
  os << "\\begin{tikzpicture}[node distance=1.5cm]\n";
  const double radius = 2.0;
  const double pi = 3.14159265358979323846;
  std::array<std::array<double, 2>, 7> pos{};
  pos[0] = {0.0, 0.0};
  for (int t = 0; t < 3; ++t)
    {
      const double theta0 = (2 * pi / 3.0) * static_cast<double>(t);
      pos[1 + 2 * t] = {radius * std::cos(theta0 - 0.3),
                        radius * std::sin(theta0 - 0.3)};
      pos[2 + 2 * t] = {radius * std::cos(theta0 + 0.3),
                        radius * std::sin(theta0 + 0.3)};
    }
 
  for (std::size_t n = 0; n < 7; ++n)
    {
      const char *colour = lat.at_node(n) != 0 ? "red!60" : "blue!60";
      os << "  \\node[circle, draw, fill=" << colour
         << ", inner sep=2pt, minimum size=6mm] (n" << n << ") at (" << pos[n][0]
         << ", " << pos[n][1] << ") {" << n << "};\n";
    }
  // Edges (deduplicated by always going low->high).
  for (std::size_t a = 0; a < 7; ++a)
    for (std::size_t b : lat.neighbours(a))
      if (b > a)
        os << "  \\draw (n" << a << ") -- (n" << b << ");\n";
  os << "\\end{tikzpicture}\n";
  return os.str();
}
 
}  // namespace
 
int main()
{
  Graph_Lattice<int> seed(build_bowtie(), 0);
  // Polarise: hub at 0, alternate triangles biased.
  seed.set_node(0, 0);
  seed.set_node(1, 1); seed.set_node(2, 1);
  seed.set_node(3, 0); seed.set_node(4, 0);
  seed.set_node(5, 1); seed.set_node(6, 1);
 
  std::printf("Aleph::CA Phase-6 example: voter model on a 7-node bowtie graph\n");
  print_state(seed, 0);
 
  Graph_Synchronous_Engine<Graph_Lattice<int>, Voter_Rule> eng(seed, Voter_Rule{2026});
 
  // Run, sampling the state every 50 steps and stopping when we
  // detect consensus.
  bool consensus = false;
  for (std::size_t s = 1; s <= 5000; ++s)
    {
      eng.step();
      if ((s % 200) == 0 or s == 1)
        print_state(eng.frame(), s);
      bool all_eq = true;
      const int v0 = eng.frame().at_node(0);
      for (std::size_t n = 1; n < eng.frame().size(); ++n)
        if (eng.frame().at_node(n) != v0)
          {
            all_eq = false;
            break;
          }
      if (all_eq)
        {
          consensus = true;
          std::printf("Consensus on value %d reached at step %zu\n", v0, s);
          print_state(eng.frame(), s);
          break;
        }
    }
  if (not consensus)
    {
      std::printf("Did not reach consensus within 5000 steps; final state:\n");
      print_state(eng.frame(), 5000);
    }
 
  std::printf("\n--- TikZ render of final state ---\n");
  std::fputs(render_tikz(eng.frame()).c_str(), stdout);
  return 0;
}