Author: Ed

The relatively low bandwidth of the amplified noise means two successive samples (measured in Arduino time) will be highly correlated. Rather than putz around with variable delays between the samples, I stuffed the noise directly into the Arduino’s MISO pin and collected four bytes of data while displaying a single row:

unsigned long UpdateLEDs(byte i) {
	
unsigned long NoiseData = 0ul;
	
	NoiseData |= (unsigned long) SendRecSPI(~LEDs[i].ColB);				// correct for low-active outputs
	NoiseData |= ((unsigned long) SendRecSPI(~LEDs[i].ColG)) << 8;
	NoiseData |= ((unsigned long) SendRecSPI(~LEDs[i].ColR)) << 16;
	NoiseData |= ((unsigned long) SendRecSPI(~LEDs[i].Row))  << 24;

	analogWrite(PIN_DIMMING,LEDS_OFF);			// turn off LED to quench current
	PulsePin(PIN_LATCH);						// make new shift reg contents visible
	analogWrite(PIN_DIMMING,LEDS_ON);

	return NoiseData;
}

The bit timing looks like this:

The vertical cursors mark the LSB position in the first and last bytes of the SPI clock. The horizontal cursors mark the minimum V_IH and maximum V_IL, so the sampled noise should produce 0 and 1 bits at the vertical cursors. Note that there’s no shift register on the input: MISO just samples the noise signal at each rising clock edge.

I picked those two bit positions because they produce more-or-less equally spaced samples during successive rows; you can obviously tune the second bit position for best picture as you see fit.

Given a pair of sequential samples, a von Neumann extractor whitens the noise and returns at most one random bit:

#define VNMASK_A 0x00000001
#define VNMASK_B 0x01000000

enum sample_t {VN_00,VN_01,VN_10,VN_11};

typedef struct {
	byte BitCount;					// number of bits accumulated so far
	unsigned Bits;					// random bits filled from low order upward
	int Bias;						// tallies 00 and 11 sequences to measure analog offset
   unsigned SampleCount[4];	// number of samples in each bin
} random_t;

random_t RandomData;

... snippage ...

byte ExtractRandomBit(unsigned long RawSample) {
	
byte RetVal;

	switch (RawSample & (VNMASK_A | VNMASK_B)) {
	case 0:							// 00 - discard
		RetVal = VN_00;
		RandomData.Bias--;
		break;
	case VNMASK_A:					// 10 - true
		RetVal = VN_10;
		RandomData.BitCount++;
		RandomData.Bits = (RandomData.Bits << 1) | 1;
		break;
	case VNMASK_B:					// 01 - false
		RetVal = VN_01;
		RandomData.BitCount++;
		RandomData.Bits  = RandomData.Bits << 1;
		break;
	case (VNMASK_A | VNMASK_B):		// 11 - discard
		RetVal = VN_11;
		RandomData.Bias++;
		break;
	}
	
	RandomData.Bias = constrain(RandomData.Bias,-9999,9999);
	RandomData.SampleCount[RetVal]++;
	RandomData.SampleCount[RetVal] = constrain(RandomData.SampleCount[RetVal],0,63999);

	return RetVal;
}

The counters at the bottom track some useful statistics.

You could certainly use something more complex, along the lines of a hash function or CRC equation, to whiten the noise, although that would eat more bits every time.

The main loop blips a pin to show when the extractor discards a pair of identical bits, as in this 11 sequence:

That should happen about half the time, which it pretty much does:

The cursors mark the same voltages and times; note the slower sweep. The middle trace blips at the start of the Row 0 refresh.

On the average, the main loop collects half a random bit during each row refresh and four random bits during each complete array refresh. Eventually, RandomData.Bits will contain nine random bits, whereupon the main loop updates the color of a single LED, which, as before, won’t change 1/8 of the time.

The Arduino trundles around the main loop every 330 µs and refreshes the entire display every 2.6 ms = 375 Hz. Collecting nine random bits requires 9 x 330 µs = 3 ms, so the array changes slightly less often than every refresh. It won’t completely change every 64 x 8/7 x 3 ms = 220 ms, because dupes, but it’s way sparkly.

In the spirit of “Video or it didn’t happen!”, there’s a low-budget Youtube video about that…