Step by Step solution about How to resolve the algorithm Elementary cellular automaton/Random number generator step by step in the Julia programming language

This Julia code is a function called evolve that simulates the evolution of a cellular automaton according to a given rule. Here's a detailed explanation of the code:

1. evolve(state, rule, N=64): This is the main function that takes three parameters:

   • state: The initial state of the cellular automaton, represented as a 64-bit integer (UInt64).
   • rule: The rule to be applied to evolve the cellular automaton, represented as a 32-bit integer (UInt32).
   • N: The number of cells in the cellular automaton. The default value is 64.

2. B(x) = UInt64(1) << x: This creates a function B that takes an 8-bit integer x and returns a 64-bit integer with a single bit set to 1 at the x-th position. This function is used to create bitmasks for extracting individual bits from the state.

3. The outer loop iterates over p from 0 to 9:

   • The purpose of this loop is to apply the rule to each bit in the state 10 times.

4. Inside the outer loop, there is an inner loop that iterates over q from 7 to 0:

   • This inner loop applies the rule to each of the 8 bits of the state, starting from the most significant bit.

5. Within the inner loop:

   • st = UInt64(state): Converts the state from a 64-bit integer to an 8-bit integer.
   • b |= (st & 1) << q: Extracts the q-th bit of the state and shifts it left by q positions, then bitwise ORs it with the previous value of b.
   • state = UInt64(0): Resets the state to 0.
   • The next loop iterates over each of the N cells in the cellular automaton:
     • t1 = (i > 0) ? st >> (i - 1) : st >> (N - 1): Calculates the bit to the left of the current cell (if it exists).
     • t2 = (i == 0) ? st << 1 : (i == 1) ? st << (N - 1) : st << (N + 1 - i): Calculates the bit to the right of the current cell (if it exists).
     • if UInt64(rule) & B(7 & (t1 | t2)) != 0: Checks if the rule specified by the rule parameter is satisfied for the current cell and its neighbors.
       • UInt64(rule) & B(7 & (t1 | t2)) != 0: This expression uses bitwise AND (&) and bitwise OR (|) to determine if the specified rule is satisfied. It checks if the bit at the q-th position in the rule (obtained by 7 & (t1 | t2)) is set to 1.
       • If the rule is satisfied, it means that the cell will be set to 1 in the next generation.
       • state |= B(i): Sets the i-th bit of the state to 1 if the rule is satisfied.

6. After applying the rule to all 8 bits and all N cells, the updated state is printed as a binary bitmask.

7. The function prints the evolved state for 10 generations.

To use this function, you would call it like this:

evolve(1, 30)

This would simulate the evolution of a cellular automaton with an initial state of 1 and a rule of 30 (also known as the Rule 30 cellular automaton) for 10 generations. The output would be a sequence of 10 binary bitmasks, each representing the state of the cellular automaton at that generation.

function evolve(state, rule, N=64)
    B(x) = UInt64(1) << x
    for p in 0:9
        b = UInt64(0)
        for q in 7:-1:0
            st = UInt64(state)
            b |= (st & 1) << q
            state = UInt64(0)
            for i in 0:N-1
                t1 = (i > 0) ? st >> (i - 1) : st >> (N - 1)
                t2 = (i == 0) ? st << 1 : (i == 1) ? st << (N - 1) : st << (N + 1 - i)
                if UInt64(rule) & B(7 & (t1 | t2)) != 0
                    state |= B(i)
                end
            end
        end
        print("$b ")
    end
    println()
end

evolve(1, 30)