1D Simplex noise for realistic LED glow

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1

Hi all,

First time poster.

Perlin made the Perlin noise generator 2001 and then improved it to "Simplex noise" for less computional overhead and easier usage in higher dimensions, Simplex noise - Wikipedia

Here is very good explanation of the algoithm (from my old University, yay!): http://weber.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf

I ported the C# implementation by Benjamin Ward, GitHub - WardBenjamin/SimplexNoise: C# Simplex Noise (1D, 2D, 3D). Supports arbitrary sizes and scales.

Demo gif: Imgur: The magic of the Internet

#include <math.h>

float x;
int o3,o5,o6;
byte perm[] = {   151,160,137,91,90, 15,131, 13,201,95,96,
53,194,233, 7,225,140,36,103,30,69,142, 8,99,37,240,21,10,23,190, 6,
148,247,120,234,75, 0,26,197,62,94,252,219,203,117, 35,11,32,57,177,
33,88,237,149,56,87,174,20,125,136,171,168,68,175,74,165,71,134,139,
48,27,166, 77,146,158,231,83,111,229,122, 60,211,133,230,220,105,92,
41,55,46,245,40,244,102,143,54,65,25,63,161, 1,216,80,73,209,76,132,
187,208, 89, 18,169,200,196,135,130,116,188,159, 86,164,100,109,198,
173,186, 3,64,52,217,226,250,124,123,5,202,38,147,118,126,255,82,85,
212,207,206, 59,227, 47,16,58,17,182,189, 28,42,223,183,170,213,119,
248,152,2,44,154,163,70,221,153,101,155,167,43,172, 9,129,22,39,253,
19,98,108,110,79,113,224,232,178,185,112,104,218,246, 97,228,251,34,
242,193,238,210,144,12,191,179,162,241,81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,
150,254,138,236,205, 93,222,114, 67,29,24, 72,243,141,128,195,78,66,
215,61,156,180
};

void setup()
{
 pinMode(3,OUTPUT);
 pinMode(5,OUTPUT);
 pinMode(6,OUTPUT);
 analogWrite(3,0);
 analogWrite(5,0);
 analogWrite(6,0);
}

void loop()
{
 x = float(millis())/200.0f;
 o3 = fastFloor(128*generate(x + 19082) + 128);
 o5 = fastFloor(128*generate(x + 5728) + 128);
 o6 = fastFloor(128*generate(x) + 128);
 analogWrite(3, o3);
 analogWrite(5, o5);
 analogWrite(6, o6);
 delay(1);
}

float generate(float x)
{
  int i0 = fastFloor(x);
  int i1 = i0 + 1;
  float x0 = x - i0;
  float x1 = x0 - 1.0f;

  float n0, n1;

  float t0 = 1.0f - x0 * x0;
  t0 *= t0;
  n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);

  float t1 = 1.0f - x1 * x1;
  t1 *= t1;
  n1 = t1 * t1 * grad(perm[i1 & 0xff], x1);
  // The maximum value of this noise is 8*(3/4)^4 = 2.53125
  // A factor of 0.395 scales to fit exactly within [-1,1]
  return 0.395f * (n0 + n1);
}

int fastFloor(float x)
{
  return (x > 0) ? ((int)x) : (((int)x) - 1);
}

float grad(int hash, float x)
{
    int h = hash & 15;
    float grad = 1.0f + (h & 7);    // Gradient value 1.0, 2.0, ..., 8.0
    if ((h & 8) != 0) grad = -grad; // Set a random sign for the gradient
    return (grad * x);              // Multiply the gradient with the distance
}
2

Interesting. Never heard of SimplexNoise or Perlin method before, so it was good to learn something reading the background papers.

Seems to generate a reasonable 'flickering candle' effect as a 1D, better than most I have seen.

Where did you get and what is the purpose of the magic numbers 19082 and 5728 in your code?

3

Amazing :smiley:

4

marco_c:
Where did you get and what is the purpose of the magic numbers 19082 and 5728 in your code?

Those are random offsets to make the three analog outputs not flicker in the exact same way.

I rewrote that part and used an ordinary int counter instead of millis().

The reason I rewrote it was that this line:
o3 = fastFloor(128*generate(x + 19082) + 128);

When it reached 2^15 that output "stalled" and only went between 0 and 1. I didn't have time to investigate further so I just skipped millis() and went with a counter that I reset before it reaches 2 ^15.