Step by Step solution about How to resolve the algorithm Elementary cellular automaton step by step in the C++ programming language

This C++ program simulates the evolution of a one-dimensional cellular automaton according to a specific rule (rule 30 in this case).

cellular automaton is a system composed of a grid of cells, each of which can be in one of several states. The states of the cells evolve over time based on a set of rules that depend on the states of the neighboring cells.

Rule 30 is a specific rule for cellular automata, which specifies the new state of a cell based on the states of its two neighbors. In this case, the rule is implemented by the RULE_TEST macro, which takes a bitmask representing the states of the three cells (the current cell and its two neighbors) and returns 1 if the new state should be 1, and 0 otherwise.

The program begins by initializing a bitset, called state, to represent the initial state of the cellular automaton. The bitset is initialized with a single 1 bit in the middle, representing a single "on" cell.

The evolve function, takes the current state of the cellular automaton, represented by the bitset state, and updates it based on the specified rule. The function iterates over each cell in the bitset, and for each cell, it calculates the new state of the cell based on the states of its two neighbors. The new state is stored in a temporary bitset called t, and then the original bitset state is updated with the new values from t.

The show function is used to print the current state of the cellular automaton to the console. It iterates over the bitset state and prints a '#' character for each 1 bit (representing an "on" cell) and a ' ' character for each 0 bit (representing an "off" cell).

The main function sets up the initial state of the cellular automaton and then calls the evolve function 10 times to simulate 10 generations of evolution. After each generation, the show function is called to print the current state of the cellular automaton to the console.

The output of the program will show the evolution of the cellular automaton over time, based on rule 30. The initial state is a single "on" cell in the middle of the bitset. As the cellular automaton evolves, the "on" cells spread out and form patterns that eventually fill the entire bitset.

#include <bitset>
#include <stdio.h>

#define SIZE	           80
#define RULE               30
#define RULE_TEST(x)       (RULE & 1 << (7 & (x)))

void evolve(std::bitset<SIZE> &s) {
    int i;
    std::bitset<SIZE> t(0);
    t[SIZE-1] = RULE_TEST( s[0] << 2 | s[SIZE-1] << 1 | s[SIZE-2] );
    t[     0] = RULE_TEST( s[1] << 2 | s[     0] << 1 | s[SIZE-1] );
    for (i = 1; i < SIZE-1; i++)
	t[i] = RULE_TEST( s[i+1] << 2 | s[i] << 1 | s[i-1] );
    for (i = 0; i < SIZE; i++) s[i] = t[i];
}
void show(std::bitset<SIZE> s) {
    int i;
    for (i = SIZE; --i; ) printf("%c", s[i] ? '#' : ' ');
    printf("\n");
}
int main() {
    int i;
    std::bitset<SIZE> state(1);
    state <<= SIZE / 2;
    for (i=0; i<10; i++) {
	show(state);
	evolve(state);
    }
    return 0;
}