How does the sierpinski fractal relate to the rain effect?

"wake up! 16b" (Outline Demoparty, May 2026, Ommen, NL) is a 16-byte MS-DOS production that uses video memory to calculate a Sierpinski fractal and play it as audio.

Video: https://youtu.be/MvycyU-kLjg | Pouet: https://www.pouet.net/prod.php?which=106210

The 16-Byte Code:

  int 10h          ; Init Video Mode 0
  mov bh, 0xb8     ; Setup VRAM segment
  mov ds, bx
  L: lodsb         ; Load [SI] to AL, inc SI
  sub si, 57       ; Move pointer backward
  xor [si], al     ; Cellular Automaton
  out 61h, al      ; PC Speaker output
  jmp short L      ; Infinite loop

1. The Canvas: `int 10h` primes the 40x25 text grid uniformly with ASCII 0x20 and color 0x07. This stable, uniform void is necessary to prevent the cellular automaton from shattering into static.

2. The Fractal (Rule 60): If this loop used `add`, it would create a binomial prefix sum:

   A^(p)[k] = 2 \* C(k+p, p-1) mod 256

But substituting `add` with `xor` discards the arithmetic carry, isolating the bit-planes. This turns the math into a pure cellular automaton mapping to Wolfram's Rule 60:

   Cell^(p)[k] = Cell^(p-1)[k] XOR Cell^(p)[k-1]

Visualizing Bit 1 propagation over 5 passes (X = set):

  P1: X X X X X X X X
  P2: . X . X . X . X
  P3: X . . X X . . X
  P4: . . . X . . . X
  P5: X X X . . . . X
  P6: . X . . . . . X
  P7: X . . . . . . X

3. The Audio: Port `61h` uses Bit 1 to physically move the PC speaker cone. The Sierpinski geometry acts directly as a square-wave audio instruction: alternating bits (like P2) yield high frequencies, while sparse rows (P4) create rhythmic rests.

4. The -56 Byte Step: The pointer's net movement is -56 bytes per loop. - Visuals: On an 80-byte wide grid, this offset shears the fractal diagonally into 10 evenly spaced, ascending vertical pillars. - Audio: 56 does not divide the 64KB segment evenly, requiring 8,192 steps (7 full wraps) to complete a cycle. Doubling the macro-cycle halves the fundamental frequency, dropping the audio exactly one octave.

5. Hardware Quirks: The theoretical math expects zeroed memory, but the XOR operation violently collides with the BIOS's 0x20/0x07 initialization. This mutates the pure triangles into a cascade of pseudo-random ASCII glyphs. Because it relies entirely on raw RAM states, the visual and auditory output is highly sensitive to the specific machine or emulator, turning a simple mathematical quirk into a unique audiovisual fingerprint.