Simulation of Chaotic Systems Gaming Project in C++

#include <iostream>
#include <vector>
#include <iomanip>

// Constants
const int ITERATIONS = 100;
const double INITIAL_VALUE = 0.5;
const double R_MIN = 2.5;
const double R_MAX = 4.0;
const double R_STEP = 0.1;

// LogisticMap class
class LogisticMap {
public:
    LogisticMap(double r, double initialValue)
        : r(r), x(initialValue) {}

    void iterate() {
        x = r * x * (1 - x);
    }

    double getValue() const {
        return x;
    }

private:
    double r; // Control parameter
    double x; // Current value
};

// Main function
int main() {
    std::vector<double> rValues;

    // Iterate over the range of r values
    for (double r = R_MIN; r <= R_MAX; r += R_STEP) {
        LogisticMap logisticMap(r, INITIAL_VALUE);

        std::cout << "r = " << std::fixed << std::setprecision(1) << r << ": ";
        
        // Generate and print the logistic map values
        for (int i = 0; i < ITERATIONS; ++i) {
            logisticMap.iterate();
            std::cout << logisticMap.getValue() << ' ';
        }
        
        std::cout << std::endl;
    }

    return 0;
}

#include <iostream>

#include <vector>

#include <iomanip>

// Constants

const int ITERATIONS = 100;

const double INITIAL_VALUE = 0.5;

const double R_MIN = 2.5;

const double R_MAX = 4.0;

const double R_STEP = 0.1;

// LogisticMap class

class LogisticMap {

public:

LogisticMap(double r, double initialValue)

: r(r), x(initialValue) {}

void iterate() {

x = r * x * (1 - x);

}

double getValue() const {

return x;

}

private:

double r; // Control parameter

double x; // Current value

};

// Main function

int main() {

std::vector<double> rValues;

// Iterate over the range of r values

for (double r = R_MIN; r <= R_MAX; r += R_STEP) {

LogisticMap logisticMap(r, INITIAL_VALUE);

std::cout << "r = " << std::fixed << std::setprecision(1) << r << ": ";

// Generate and print the logistic map values

for (int i = 0; i < ITERATIONS; ++i) {

logisticMap.iterate();

std::cout << logisticMap.getValue() << ' ';

}

std::cout << std::endl;

}

return 0;

}

Explanation:

LogisticMap Class:
- r: The control parameter for the logistic map, which influences the chaotic behavior.
- x: The current value of the system, initialized with the initialValue.
- LogisticMap(double r, double initialValue): Constructor that sets the value of r and initializes x.
- iterate(): Updates the value of x using the logistic map formula $xn+1=r⋅xn⋅(1−xn)x_{n+1} = r \cdot x_n \cdot (1 – x_n)$ .
- getValue() const: Returns the current value of x.
Main Function:
- Creates a range of r values from R_MIN to R_MAX with a step size of R_STEP.
- For each r value, it initializes a LogisticMap object with the current r and INITIAL_VALUE.
- Iterates the logistic map and prints the resulting values to show how the system evolves for different values of r.

Simulation of Chaotic Systems Gaming Project in C++

Explanation:

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