Name	Name	Last commit message	Last commit date
parent directory ..
img	img
README.md	README.md
async_automata.lua	async_automata.lua
binary_space_partition.lua	binary_space_partition.lua
bubbles.lua	bubbles.lua
cellular_automata.lua	cellular_automata.lua
convex_hull.lua	convex_hull.lua
corridors.lua	corridors.lua
gallery.lua	gallery.lua
isolines.lua	isolines.lua
maxrectangle.lua	maxrectangle.lua
perlin.lua	perlin.lua
readme.lua	readme.lua
sampling.lua	sampling.lua
voronoi.lua	voronoi.lua

forma example gallery

Binary space partitioning
Convex hull finder
Voronoi tessellation
Perlin noise sampling
Maximum rectangle finding
Circle primitives
Cellular automata
Sampling methods
Rasterising isolines
Combining cellular automata rules
Readme example
Asynchronous cellular automata

Binary space partitioning

local subpattern = require('forma.subpattern')
local primitives = require('forma.primitives')

-- Generate an 80x20 square and partition it into segments of maximally 50 cells
local square = primitives.square(80,20)
local bsp = subpattern.bsp(square, 50)

-- Print resulting pattern segments
subpattern.print_patterns(square,bsp)

Output

Convex hull finder

This generates a messy random pattern, and finds its convex hull.

local subpattern = require('forma.subpattern')
local primitives = require('forma.primitives')

-- Generate a domain and a random set of points
local domain = primitives.square(80, 20)
local points = subpattern.random(domain, 30)

-- Find the convex hull
local c_hull = subpattern.convex_hull(points)
subpattern.print_patterns(domain,{c_hull, points}, {'x', 'o'})

Output

Voronoi tessellation

local cell       = require('forma.cell')
local primitives = require('forma.primitives')
local subpattern = require('forma.subpattern')

-- Generate a random pattern in a specified domain
local sq = primitives.square(80,20)
local rn = subpattern.random(sq, 10)

-- Compute the corresponding voronoi tesselation
local measure  = cell.chebyshev
local segments = subpattern.voronoi(rn, sq, measure)

subpattern.print_patterns(sq, segments)

Output

Perlin noise sampling

Here we sample a square domain pattern according to perlin noise, generating three new patterns consisting of the noise thresholded at values of 0, 0.5 and 0.7.

local subpattern = require('forma.subpattern')
local primitives = require('forma.primitives')

local domain = primitives.square(80,20)
local frequency, depth = 0.2, 1
local thresholds = {0, 0.5, 0.7}
local noise  = subpattern.perlin(domain, frequency, depth, thresholds)

-- Print resulting pattern segments
subpattern.print_patterns(domain, noise, {'.', '+', 'o'})

Output

Maximum rectangle finding

This generates a messy random pattern, and finds the largest contiguous rectangle of active cells within it.

local subpattern = require('forma.subpattern')
local primitives = require('forma.primitives')

-- Generate a domain and a messy 'blocking' pattern
local domain = primitives.square(80, 20)
local blocks = subpattern.random(domain, 80)

-- Find the largest contiguous 'unblocked' rectangle in the base pattern
local mxrect = subpattern.maxrectangle(domain - blocks)
subpattern.print_patterns(domain,{blocks, mxrect}, {'o','#'})

Output

Circle primitives

local cell       = require('forma.cell')
local pattern    = require('forma.pattern')
local primitives = require('forma.primitives')
local subpattern = require('forma.subpattern')

local max_radius = 4

-- Setup domain and some random seeds
local domain = primitives.square(80,20)
local seeds  = subpattern.poisson_disc(domain, cell.euclidean, 2*max_radius)
local shapes = pattern.new()

-- Randomly generate some circles in the domain
for seed in seeds:cells() do
    local circle = primitives.circle(math.random(2, max_radius))
    shapes = shapes + circle:shift(seed.x, seed.y)
end

subpattern.print_patterns(domain, {shapes}, {'o'})

Output

Cellular automata

Demonstration of classic cellular-automata cave generation (4-5 rule).

local primitives    = require('forma.primitives')
local subpattern    = require('forma.subpattern')
local automata      = require('forma.automata')
local neighbourhood = require('forma.neighbourhood')

-- Domain for CA
local sq = primitives.square(80,20)

-- CA initial condition: sample at random from the domain
local ca = subpattern.random(sq, 800)

-- Moore neighbourhood 4-5 rule
local moore = automata.rule(neighbourhood.moore(), "B5678/S45678")
local ite, converged = 0, false
while converged == false and ite < 1000 do
    ca, converged = automata.iterate(ca, sq, {moore})
    ite = ite+1
end

-- Print to stdout
subpattern.print_patterns(sq, {ca}, {'#'})

Output

Sampling methods

Demonstrations of various methods for sampling from a pattern.

pattern.random generates white noise, it's fast and irreguarly distributed.
Lloyd's algorithm when a specific number of uniform samples are desired.
Mitchell's algorithm is a good (fast) approximation of (2).
Poisson-disc when a minimum separation between samples is the only requirement.

local cell          = require('forma.cell')
local subpattern    = require('forma.subpattern')
local primitives    = require('forma.primitives')

-- Domain and seed
local measure = cell.chebyshev
local domain   = primitives.square(80,20)

-- Random samples, uncomment these turn by turn to see the differences
local random  = subpattern.poisson_disc(domain, measure, 4)
--local random  = subpattern.mitchell_sample(domain, measure, 100, 100)
--local random   = subpattern.random(domain, 40)
--local _, random = subpattern.voronoi_relax(random, domain, measure)

subpattern.print_patterns(domain, {random}, {'#'})

Output

Rasterising isolines

Here we generate a pattern randomly filled with points, and take as a scalar field N(cell) = F_2(cell) - F_1(cell), where F_n is the Chebyshev distance to the nth nearest neighbour. Isolines at N = 0 are drawn by thresholding N at 1 and taking the surface.

local cell          = require('forma.cell')
local subpattern    = require('forma.subpattern')
local primitives    = require('forma.primitives')

-- Distance measure
local measure = cell.chebyshev

-- Domain and list of seed cells
local sq = primitives.square(80,20)
local rn = subpattern.random(sq, 20):cell_list()

-- Worley noise mask
local mask = function(tcell)
    local sortfn = function(a,b)
        return measure(tcell, a) < measure(tcell, b)
    end
    table.sort(rn, sortfn)
    local F1 = measure(rn[1], tcell)
    local F2 = measure(rn[2], tcell)
    return F2 - F1  > 1
end

-- Compute the thresholded pattern and print its surface
local noise = subpattern.mask(sq, mask)
subpattern.print_patterns(sq, {noise:surface()}, {'#'})

Output

Combining cellular automata rules

Here the way multiple CA rules can be combined into a single ruleset is demonstrated. A asynchronous cellular automata with a complicated ruleset generates an interesting 'corridor' like pattern.

local primitives    = require('forma.primitives')
local automata      = require('forma.automata')
local subpattern    = require('forma.subpattern')
local neighbourhood = require('forma.neighbourhood')

-- Generate a domain, and an initial state ca with one random seed cell
local domain = primitives.square(80,20)
local ca = subpattern.random(domain, 1)

-- Complicated ruleset, try leaving out or adding more rules
local moore = automata.rule(neighbourhood.moore(),      "B12/S012345678")
local diag  = automata.rule(neighbourhood.diagonal_2(), "B01/S01234")
local vn    = automata.rule(neighbourhood.von_neumann(),"B12/S01234")
local ruleset = {vn, moore, diag}

repeat
    local converged
    ca, converged = automata.async_iterate(ca, domain, ruleset)
until converged

local nbh = neighbourhood.von_neumann()
local segments = subpattern.neighbourhood_categories(ca, nbh)
subpattern.print_patterns(domain, segments, nbh:category_label())

Output

Readme example

This generates the example used in the readme. Runs a 4-5 rule CA for 'cave generation and then computes the contiguous sub-patterns and prints them.

-- Load forma modules, lazy init is also available, i.e
-- require('forma')
local primitives    = require('forma.primitives')
local subpattern    = require('forma.subpattern')
local automata      = require('forma.automata')
local neighbourhood = require('forma.neighbourhood')

-- Generate a square box to run the CA inside
local domain = primitives.square(80,20)

-- CA initial condition: 800-point random sample of the domain
local ca = subpattern.random(domain, 800)

-- Moore (8-cell) neighbourhood 4-5 rule
local moore = automata.rule(neighbourhood.moore(), "B5678/S45678")

-- Run the CA until converged or 1000 iterations
local ite, converged = 0, false
while converged == false and ite < 1000 do
    ca, converged = automata.iterate(ca, domain, {moore})
    ite = ite+1
end

-- Access a subpattern's cell coordinates for external use
for icell in ca:cells() do
    -- local foo = bar(icell)
    -- or
    -- local foo = bar(icell.x, icell.y)
end

-- Find all 4-contiguous segments of the CA pattern
-- Uses the von-neumann neighbourhood to determine 'connectedness'
-- but any custom neighbourhood can be used)
local segments = subpattern.segments(ca, neighbourhood.von_neumann())

-- Print a representation to io.output
subpattern.print_patterns(domain, segments)

Output

Asynchronous cellular automata

Here the use of an asynchronous cellular automata is demonstrated, making use also of symmetrisation methods to generate a final, symmetric pattern.

local pattern       = require('forma.pattern')
local primitives    = require('forma.primitives')
local automata      = require('forma.automata')
local subpattern    = require('forma.subpattern')
local neighbourhood = require('forma.neighbourhood')

-- Domain for CA to operate in
local sq = primitives.square(10,5)

-- Make a new pattern consisting of a single random cell from the domain
local start_point = sq:rcell() -- Select a random point
local ca_pattern  = pattern.new():insert(start_point.x, start_point.y)

-- Moore neighbourhood rule for CA
local moore = automata.rule(neighbourhood.moore(), "B12/S012345678")

-- Perform asynchronous CA update until convergence
local converged = false
while converged == false do
    ca_pattern, converged = automata.async_iterate(ca_pattern, sq, {moore})
end

-- Add some symmetry by mirroring the basic pattern a couple of times
local symmetrised_pattern = ca_pattern:hreflect()
symmetrised_pattern = symmetrised_pattern:vreflect():vreflect()
symmetrised_pattern = symmetrised_pattern:hreflect():hreflect()

-- Categorise the pattern according to possible vN neighbours and print to screen
-- This turns the basic pattern into standard 'box-drawing' characters
local vn = neighbourhood.von_neumann()
local segments = subpattern.neighbourhood_categories(symmetrised_pattern, vn)
subpattern.print_patterns(symmetrised_pattern, segments, vn:category_label())

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examples

examples

README.md

forma example gallery

Binary space partitioning

Output

Convex hull finder

Output

Voronoi tessellation

Output

Perlin noise sampling

Output

Maximum rectangle finding

Output

Circle primitives

Output

Cellular automata

Output

Sampling methods

Output

Rasterising isolines

Output

Combining cellular automata rules

Output

Readme example

Output

Asynchronous cellular automata

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README.md

forma example gallery

Binary space partitioning

Output

Convex hull finder

Output

Voronoi tessellation

Output

Perlin noise sampling

Output

Maximum rectangle finding

Output

Circle primitives

Output

Cellular automata

Output

Sampling methods

Output

Rasterising isolines

Output

Combining cellular automata rules

Output

Readme example

Output

Asynchronous cellular automata

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