Generate Logic Life Search (LLS) input grid for finding spaceships and oscillators, with additional features not yet supported natively by LSS (like strobing background and gradually moving search area).

make_lls_grid.py

#!/usr/bin/python

import re
import sys
import argparse

def fail(msg):
    sys.stderr.write(sys.argv[0] + ": " + msg + "\n")
    sys.exit(1)

parser = argparse.ArgumentParser(description="Generate LLS input grid for finding spaceships and oscillators.")
parser.add_argument('width', type=int, help="width of pattern bounding box")
parser.add_argument('height', type=int, help="height of pattern bounding box")
parser.add_argument('-f', '--first-gen', type=int, nargs=2, help="width and height of first generation")
parser.add_argument('-p', '--period', type=int, default=2, help="period until first generation reappears")
parser.add_argument('-x', '--shift-x', type=int, default=0, help="horizontal shift over period")
parser.add_argument('-y', '--shift-y', type=int, default=0, help="vertical shift over period")
parser.add_argument('-m', '--mirror', choices=("", "none", "x", "y", "d", "diag", "a", "antidiag", "9", "90", "1", "180", "2", "270"), help="mirror or rotate pattern after period")
parser.add_argument('--fixed', nargs='+', default=[], help="fixed cell values in initial pattern (e.g. \"a1=1 a2=b1=b2=0\"")
parser.add_argument('--wide', action='store_true', help="allow intermediate generations to use the whole (width+x)*(height+y) cell area")
parser.add_argument('--strobe', action='store_true', help="use a strobing background for B0 rules")
args = parser.parse_args()

# validate pattern dimensions
if args.period < 1:
    fail("Period must be positive.")
if args.strobe and args.period % 2:
    fail("Period must be even for strobing rules.")
if args.width < 1 or args.height < 1:
    fail("Width and height must be at least 1.")

if args.first_gen is None:
    gen0_width  = args.width
    gen0_height = args.height
else:
    gen0_width, gen0_height = args.first_gen
    if gen0_width < 1 or gen0_height < 1:
        fail("First generation width and height must be at least 1.")
    if gen0_width > args.width or gen0_height > args.height:
        fail("First generation width and height may not be greater than for later generations.")

total_width  = args.width  + 4 + abs(args.shift_x)
total_height = args.height + 4 + abs(args.shift_y)

# glide / rotate symmetry handling
mirror_x = args.mirror in ("x", "a", "antidiag", "9", "90", "1", "180")
mirror_y = args.mirror in ("y", "a", "antidiag", "1", "180", "2", "270")
transpose = args.mirror in ("d", "diag", "a", "antidiag", "9", "90", "2", "270")

if transpose and gen0_width != gen0_height:
    fail("Only square grids are supported for --mirror=%s." % args.mirror)

# build dictionary of fixed cells
fixed = {}
for eqn in args.fixed:
    eqn = eqn.strip()
    if eqn == "": continue
    terms = eqn.split("=")
    if len(terms) < 2:
        fail("Invalid equation \"%s\" in --fixed=\"%s\"." % (eqn, args.fixed))
    val = terms.pop().strip()
    if val != "0" and val != "1":
        fail("Invalid constant \"%s\" in equation \"%s\"." % (val, eqn))
    for term in terms:
        term = term.strip()
        if not re.match(r'^[a-z]+[1-9][0-9]*$', term):
            fail("Invalid term \"%s\" in equation \"%s\"." % (term, eqn))
        if term in fixed and fixed[term] != val:
            fail("Inconsistent assignment for \"%s\" in --fixed=\"%s\"." % (term, args.fixed))
        fixed[term] = val

# helper function for generating cell symbol names
def cellname(row, col):
    name = ""
    while col >= 0:
        col, letter = divmod(col, 26)
        name = chr(ord('a') + letter) + name
        col -= 1
    return name + str(row+1)

maxlen = max(2, len(cellname(args.width-1, args.height-1)))
cellfmt = "%%-%ss" % maxlen 

for gen in range(args.period + 1):
    # initialize grid to all empty cells
    void = str(gen % 2) if args.strobe else "0"
    grid = [[void] * total_width for i in range(total_height)]
    # set fixed borders
    for row in range(total_height):
        grid[row][0] = grid[row][total_width-1] = void + "'"
    for col in range(1, total_width-1):
        grid[0][col] = grid[total_height-1][col] = void + "'"
    # draw in the search area
    if gen in (0, args.period):
        dy = 2 + (args.height - gen0_height) // 2 + max(0, args.shift_y if gen else -args.shift_y)
        dx = 2 + (args.width  - gen0_width)  // 2 + max(0, args.shift_x if gen else -args.shift_x)
        for y in range(gen0_height):
            for x in range(gen0_width):
                row = y
                col = x
                if gen and mirror_y: row = gen0_height - row - 1
                if gen and mirror_x: col = gen0_width - col - 1
                if gen and transpose: row, col = col, row
                name = cellname(row, col)
                grid[y + dy][x + dx] = fixed[name] if name in fixed else name
    else:
        if args.wide:
            top = left = 2
            bottom = total_height - 2
            right = total_width - 2
        else:
            top  = 2 + int(round(args.shift_y * gen * 1.0 / args.period))
            left = 2 + int(round(args.shift_x * gen * 1.0 / args.period))
            bottom = top  + args.height
            right  = left + args.width
        for row in range(top, bottom):
            for col in range(left, right):
                grid[row][col] = '*'
    # print output
    if gen > 0:
        print("")
    for line in grid:
        print(" ".join(cellfmt % cell for cell in line))