What is Perlin Noise?

At some point while programming you are confronted with the term Perlin or Noise or Perlin-Noise and ask yourself what kind of function it is and what is it good for!

1.) ... Example of a simple Perlin noise as a simple cloud!
2.) ... Why should I know this, do I have to understand Perlin noise!
​​3.) ... Simple Perlin noise example code in CPP

1.) Example of a simple Perlin noise as a simple cloud!

(Picture-3) Perlin-Noise Wood!

(Image-4) Clouds with Perlin noise as a function!

2.) Why do I need this knowledge? I need to understand Perlin Noise!

(Image-1) Ken Perlin and more features!

(Image-2) Perlin noise and city with or from random numbers!

3.) Simple Perlin-Noise example code in CPP

//Here's the translated and explained C++ code for generating Perlin noise, including comments on the functionality:
 
 
#include <iostream>
#include <cmath>
#include <vector>
#include <conio.h>  // For _getch to wait for a key press
 
std::vector<int> permutation = std::vector<int>(512);
 
class PerlinNoise 
{
public:
 PerlinNoise() {
  int i = 0;
  // Initialize the permutation vector with values from 0 to 255
  for (i = 0; i < 256; ++i) {
   permutation[i] = i;
  }
 
  // Shuffle the permutation vector using a custom random number generator
  int seed = 42; // You can change the seed for different patterns
  shufflePermutation(seed);
 
  // Duplicate the permutation vector to make wrapping easier
  for (i = 0; i < 256; ++i) {
   permutation[256 + i] = permutation[i];
  }
 }
 
 double noise(double x, double y, double z) const {
  int X = static_cast<int>(floor(x)) & 255;
  int Y = static_cast<int>(floor(y)) & 255;
  int Z = static_cast<int>(floor(z)) & 255;
 
  x -= floor(x);
  y -= floor(y);
  z -= floor(z);
 
  double u = fade(x);
  double v = fade(y);
  double w = fade(z);
 
  int A = permutation[X] + Y;
  int AA = permutation[A] + Z;
  int AB = permutation[A + 1] + Z;
  int B = permutation[X + 1] + Y;
  int BA = permutation[B] + Z;
  int BB = permutation[B + 1] + Z;
 
  double p1 = grad(permutation[AA], x, y, z);
  double p2 = grad(permutation[BA], x - 1, y, z);
  double p3 = grad(permutation[AB], x, y - 1, z);
  double p4 = grad(permutation[BB], x - 1, y - 1, z);
  double p5 = grad(permutation[AA + 1], x, y, z - 1);
  double p6 = grad(permutation[BA + 1], x - 1, y, z - 1);
  double p7 = grad(permutation[AB + 1], x, y - 1, z - 1);
  double p8 = grad(permutation[BB + 1], x - 1, y - 1, z - 1);
 
  double x1 = lerp(u, p1, p2);
  double x2 = lerp(u, p3, p4);
  double x3 = lerp(u, p5, p6);
  double x4 = lerp(u, p7, p8);
 
  double y1 = lerp(v, x1, x2);
  double y2 = lerp(v, x3, x4);
 
  return lerp(w, y1, y2);
 }
 
private:
 double fade(double t) const {
  return t * t * t * (t * (t * 6 - 15) + 10);
 }
 
 double lerp(double t, double a, double b) const {
  return a + t * (b - a);
 }
 
 double grad(int hash, double x, double y, double z) const {
  int h = hash & 15;
  double u = h < 8 ? x : y;
  double v = h < 4 ? y : (h == 12 || h == 14 ? x : z);
  return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
 }
 
 void shufflePermutation(int seed) {
  int size = permutation.size();
  for (int i = size - 1; i > 0; --i) {
   int j = seed % (i + 1);
   std::swap(permutation[i], permutation[j]);
  }
 }
};
 
int main() {
 PerlinNoise perlin;
 double x = 5.0, y = 10.0, z = 15.0;
 double noiseValue = perlin.noise(x, y, z);
 std::cout << "Perlin noise at (" << x << ", " << y << ", " << z << ") = " << noiseValue << std::endl;
 
 std::cout << "Press any key to continue...\n";
 
 // Wait for a key press
 _getch();
 
 return 0;
}