Step by Step solution about How to resolve the algorithm Feigenbaum constant calculation step by step in the Kotlin programming language

The provided Kotlin code implements the Feigenbaum constants calculation, which are constants that describe the behavior of chaotic systems.

Here's a detailed explanation of the code:

1. Main Function (main Function):

   • The program starts with the main function, which is the entry point of the program.
   • Inside the main function, the feigenbaum() function is called.

2. feigenbaum() Function:

   • This function calculates the Feigenbaum constants.
   • It uses a loop to iterate through different values of i (the iteration count), and within each iteration, it calculates and prints the Feigenbaum constant d.

3. Initialization of Variables:

   • maxIt is the maximum number of iterations, set to 13.
   • maxItJ is the maximum number of inner iterations, set to 10.
   • a1 and a2 are variables used in the calculation.
   • d1 is a variable used to store the previous value of d.

4. Outer Loop:

   • The outer loop iterates through values of i from 2 to maxIt.

5. Inner Loop:

   • For each value of i, an inner loop iterates through values of j from 1 to maxItJ.
   • Within this inner loop, variables x and y are used to perform calculations.

6. Calculation of a:

   • The variable a is calculated as a1 + (a1 - a2) / d1.

7. Calculation of d:

   • The variable d is calculated as (a1 - a2) / (a - a1).

8. Printing the Results:

   • The calculated value of d is printed along with the value of i in the format "%2d  %.8f".

9. Update of Variables:

   • After each iteration, the values of d1, a2, and a1 are updated for the next iteration.

Once the feigenbaum() function completes, the program exits.

The output of the program will be a table of values of i and the corresponding Feigenbaum constants d.

// Version 1.2.40

fun feigenbaum() {
    val maxIt = 13
    val maxItJ = 10
    var a1 = 1.0
    var a2 = 0.0
    var d1 = 3.2
    println(" i       d")
    for (i in 2..maxIt) {
        var a = a1 + (a1 - a2) / d1
        for (j in 1..maxItJ) {
            var x = 0.0
            var y = 0.0
            for (k in 1..(1 shl i)) {
                 y = 1.0 - 2.0 * y * x
                 x = a - x * x
            }
            a -= x / y
        }
        val d = (a1 - a2) / (a - a1)
        println("%2d    %.8f".format(i,d))
        d1 = d
        a2 = a1
        a1 = a
    }
}

fun main(args: Array<String>) {
    feigenbaum()
}