Divide and Conquer Line Algorithm for the ZX Spectrum

While attempting to write a game in 256 bytes I needed a routine to draw lines, but Bresenham's line algorithm weighs in at approx ~120 bytes. The only suitable alternative I'm aware of is recursive divide and conquer: divide a line into two smaller lines and call the draw routine with each in turn:

/* Draw a line from (ax,ay) to (bx,by) */

int draw ( ax, ay, bx, by )
{
    int midx, midy;
    midx = ( ax+bx ) / 2;
    midy = ( ay+by ) / 2;
    if ( midx != ax && midy != ay )
    {
        draw( midx, midy, ax, ay );
        draw( bx, by, midx, midy );
        plot( midx, midy );
    }
}

This is significantly smaller thank Bresenham's, 32 byte of Z80. However, there are a couple of compromises: it's slower and the lines aren't perfect because the rounding errors accumulate.

; draw lines using recursive divide and conquer
; from de = end1 (d = x-axis, e = y-axis)
; to   hl = end2 (h = x-axis, l = y-axis)

DRAW:
  call PLOT

  push hl

; calculate hl = centre pixel

  ld a,l
  add a,e
  rra
  ld l,a
  ld a,h
  add a,d
  rra
  ld h,a

; if de (end1) = hl (centre) then we're done

  or a
  sbc hl,de
  jr z,EXIT
  add hl,de

  ex de,hl
  call DRAW    ; de = centre, hl = end1
  ex (sp),hl
  ex de,hl
  call DRAW    ; de = end2, hl = centre

  ex de,hl
  pop de
  ret

EXIT:
  pop hl
  ret

; ---------------------------

; plot d = x-axis, e = y-axis

PLOT:
  push hl
  ld a,d
  and 7
  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,l
  xor d
  and 7
  xor d
  rrca
  rrca
  rrca
  ld l,a
  ld a,1
PLOTBIT:
  rrca
  djnz PLOTBIT
  or (hl)
  ld (hl),a
  pop hl
  ret

Alternatively the de(end1) = hl(centre) test can be replaced with a recursion depth count to create an even slower 28 byte routine:

; draw lines using recursive divide and conquer
; from de = end1 (d = x-axis, e = y-axis)
; to   hl = end2 (h = x-axis, l = y-axis)

DRAW:
  ld c,8

DRAW2:
  dec c
  jr z,EXIT

  push de

; calculate de = centre pixel

  ld a,l
  add a,e
  rra
  ld e,a
  ld a,h
  add a,d
  rra
  ld d,a

  call DRAW2   ; de = centre, hl = end1
  ex (sp),hl
  call DRAW2   ; de = centre, hl = end2

  call PLOT
  ex de,hl
  pop hl
EXIT:
  inc c
  ret

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