Friday, 27 May 2016

Langton's Ant for the ZX Spectrum

Langton's Ant is an automata which creates a complex pattern by following a couple of simple rules:

  • If the ant is on an empty pixel, turn 90° right, set the pixel then move forward
  • If the ant is on a set pixel, turn 90° left, reset the pixel then move forward

The ant's path appears chaotic at first before falling into a repetitive “highway” pattern, moving 2 pixels diagonally every 104 cycles.

Here's the code to display Langton's Ant on the ZX Spectrum in 61 bytes. It runs in just over a second so you might want to add a halt to slow things down:

  org 65472

  ld de,128*256+96 

ANT:
; halt
  ld a,c      ; check direction
  and 3
  rrca
  add a,a
  dec a
  jr nc,XMOVE

  add a,e     ; adjust y position +/-1
  ld e,a
  cp 192
  ret nc  
  xor a

XMOVE:
  add a,d     ; adjust x position +/-1
  ld d,a

; ----------
  and 7       ; calculate screen address
  ld b,a
  inc b
  ld a,e
  rra
  scf
  rra
  or a
  rra
  ld l,a
  xor e
  and 248
  xor e
  ld h,a
  ld a,d
  xor l
  and 7
  xor d
  rrca
  rrca
  rrca
  ld l,a
  ld a,1
PLOTBIT:
  rrca
  djnz PLOTBIT
; ----------

  ld b,a      ; test pixel
  and (hl)

  jr nz,LEFT  ; turn left/right
  inc c
  inc c
LEFT:
  dec c

  ld a,b      ; flip pixel
  xor (hl)
  ld (hl),a
  jr ANT

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