ZX Spectrum Koch (Lévy C) Curve

A few years ago I submitted a couple of type-in programs (C-Curve and Curtains) to Your Sinclair and they featured in the penultimate issue (August 1993).

Encouraged by a shiny new YS badge I sent off a new batch of programs. Unfortunately it was too late. The September issue would be Your Sinclair's "Big Final Issue".

C-Curve is one of the simplest fractal curves. It starts with a straight line. To find the next iteration, each line is replaced by two lines at 90°:

Here's a later 69 byte version of the program which plots the fractal in approximately 1.52 seconds! Assemble with Pasmo (pasmo ccurve.asm ccurve.bin), load the binary to address 65467 in your favourite emulator and run using RANDOMIZE USR 65467 :-)

  org 65467
  ld de,49023 ; d = position on x axis
              ; e = position on y axis
  ld bc,3840  ; b = number of iterations
              ; c = initial direction
RECURSE:
  djnz DOWN

  ld a,6      ; check direction
  and c       ; c=0, left
  rrca        ; c=2, up
  rrca        ; c=4, right
  add a,a     ; c=6, down
  dec a
  jr nc,XMOVE

  add a,e     ; adjust y position +/-1

  ld e,a      ; calculate high byte of screen pos
  rrca
  scf
  rra
  rrca
  xor e
  and 88
  xor e
  and 95
  ld h,a
  sub h

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

  ld d,a      ; calculate low byte of screen pos
  rlca
  rlca
  rlca
  xor e
  and 199
  xor e
  rlca
  rlca
  ld l,a

  ld a,7      ; calculate bit position of pixel
  and d
  ld b,a
  inc b
  ld a,1
SHIFTBIT:
  rrca
  djnz SHIFTBIT

  xor (hl)    ; plot
  ld (hl),a
  ret

DOWN:
  inc c       ; turn 45° clockwise
  call RECURSE
  inc b
  dec c       ; turn 90° anti-clockwise
  dec c
  call RECURSE
  inc b
  inc c       ; turn 45° clockwise
  ret

Finally here's a short type-in program to poke the code into a real Spectrum!