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fastnoise.go
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fastnoise.go
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// MIT License
//
// Copyright(c) 2023 Jordan Peck ([email protected])
// Copyright(c) 2023 Contributors
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files(the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions :
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//
// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll
// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo
// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd
// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx
// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx
// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd
// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo
// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo
// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo
// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo
// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo
// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo
// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl
// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c
// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c
// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc
// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll
// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo
// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd
// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk
// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000
// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX
//
// VERSION: 1.1.1
// https://github.com/Auburn/FastNoiseLite
package fastnoise
import (
"math"
)
// Float represents a floating-point number type.
type Float interface {
float32 | float64
}
// Enum types
type (
// NoiseType describes a noise algorithm.
NoiseType int
// RotationType3D describes a rotation method to apply to 3D noise.
RotationType3D int
// FractalType describes the fractal method for fractal noise types.
FractalType int
// CellularDistanceFunc describes the method for cellular distance functions.
CellularDistanceFunc int
// CellularReturnType describes the return type for cellular distance noise.
CellularReturnType int
// DomainWarpType describes the method used for domain warps.
DomainWarpType int
)
const (
OpenSimplex2 NoiseType = iota
OpenSimplex2S
Cellular
Perlin
ValueCubic
Value
TypeCount // The number of noise types
)
const (
RotationNone RotationType3D = iota
RotationImproveXYPlanes
RotationImproveXZPlanes
)
const (
FractalNone FractalType = iota
FractalFBm
FractalRidged
FractalPingPong
FractalDomainWarpProgressive
FractalDomainWarpIndependent
)
const (
CellularDistanceEuclidean CellularDistanceFunc = iota
CellularDistanceEuclideanSq
CellularDistanceManhattan
CellularDistanceHybrid
)
const (
CellularReturnCellValue CellularReturnType = iota
CellularReturnDistance
CellularReturnDistance2
CellularReturnDistance2Add
CellularReturnDistance2Sub
CellularReturnDistance2Mul
CellularReturnDistance2Div
)
const (
DomainWarpOpenSimplex2 DomainWarpType = iota
DomainWarpOpenSimplex2Reduced
DomainWarpBasicGrid
)
type (
// noise2DFunc is a prototype for a function that generates 2D noise.
noise2DFunc[T Float] func(state *State[T], seed int, x, y T) T
// noise3DFunc is a prototype for a function that generates 3D noise.
noise3DFunc[T Float] func(state *State[T], seed int, x, y, z T) T
)
// State contains the configuration for generating a noise. This should only be created
// with NewState, as it will initialize with sane defaults, including any private members.
//
// May be used to generate either float32 or float64 values.
type State[T Float] struct {
// Seed for all noise types.
//
// Default: 1337
Seed int
// Frequency for all noise types.
//
// Default: 0.01
Frequency T
// noiseType specifies the algorithm that will be used with GetNoise2D and GetNoise3D.
//
// Default: OpenSimplex2
noiseType NoiseType
// RotationType3D specified the type of rotation applied to 3D noise.
//
// Default: RotationNone
RotationType3D RotationType3D
// fractalType specifies the method used for combining octaves for all fractal noise types.
// Only effects DomainWarp2D and DomainWarp3D functions.
//
// Default: FractalNone
fractalType FractalType
// Octaves is the number of octaves used for all fractal noise types.
//
// Default: 3
Octaves int
// Lacunarity is the octave Lacunarity for all fractal noise types.
//
// Default: 2.0
Lacunarity T
// Gain is the octave gain for all fractal noise types.
//
// Default: 0.5
Gain T
// WeightedStrength is the octave weighting for all non-domain warp fractal types.
//
// Default: 0.0
WeightedStrength T
// PingPongStrength is the strength of the fractal ping pong effect.
//
// Default: 2.0
PingPongStrength T
// CellularDistanceFunc specifies the distance function used in cellular noise calculations.
//
// Default: CellularDistanceEuclideanSq,
CellularDistanceFunc CellularDistanceFunc
// CellularReturnType specifies the cellular return type from cellular noise calculations.
//
// Default: CellularReturnDistance,
CellularReturnType CellularReturnType
// CellularJitterMod is the maximum distance a cellular point can move from it's grid position.
// Setting this higher than 1 will cause artifacts.
//
// Default: 1.0
CellularJitterMod T
// DomainWarpType specifies the algorithm when using DomainWarp2D or DomainWarp3D.
//
// Default: DomainWarpOpenSimplex2
DomainWarpType DomainWarpType
// DomainWarpAmp is the maximum warp distance from original position when using DomainWarp2D
// or DomainWarp3D.
//
// Default: 1.0
DomainWarpAmp T
// noise2D contains the function used to generate 2D noise based on the state settings.
noise2D noise2DFunc[T]
// noise3D contains the function used to generate 3D noise based on the state settings.
noise3D noise3DFunc[T]
}
// Constants
var gradients2D = []float32{
0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721,
0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509,
0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381,
-0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721,
-0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509,
-0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381,
0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721,
0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509,
0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381,
-0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721,
-0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509,
-0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381,
0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721,
0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509,
0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381,
-0.130526192220052, -0.99144486137381, -0.38268343236509, -0.923879532511287, -0.608761429008721, -0.793353340291235, -0.793353340291235, -0.608761429008721,
-0.923879532511287, -0.38268343236509, -0.99144486137381, -0.130526192220052, -0.99144486137381, 0.130526192220051, -0.923879532511287, 0.38268343236509,
-0.793353340291235, 0.608761429008721, -0.608761429008721, 0.793353340291235, -0.38268343236509, 0.923879532511287, -0.130526192220052, 0.99144486137381,
0.130526192220052, 0.99144486137381, 0.38268343236509, 0.923879532511287, 0.608761429008721, 0.793353340291235, 0.793353340291235, 0.608761429008721,
0.923879532511287, 0.38268343236509, 0.99144486137381, 0.130526192220051, 0.99144486137381, -0.130526192220051, 0.923879532511287, -0.38268343236509,
0.793353340291235, -0.60876142900872, 0.608761429008721, -0.793353340291235, 0.38268343236509, -0.923879532511287, 0.130526192220052, -0.99144486137381,
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}
// ====================
// Public API
// ====================
// New initializes a new noise generator state with default values. This function must be used
// to create new states.
func New[T Float]() *State[T] {
state := &State[T]{
Seed: 1337,
Frequency: 0.01,
noiseType: OpenSimplex2,
RotationType3D: RotationNone,
fractalType: FractalNone,
Octaves: 3,
Lacunarity: 2.0,
Gain: 0.5,
WeightedStrength: 0.0,
PingPongStrength: 2.0,
CellularDistanceFunc: CellularDistanceEuclideanSq,
CellularReturnType: CellularReturnDistance,
CellularJitterMod: 1.0,
DomainWarpAmp: 30.0,
DomainWarpType: DomainWarpOpenSimplex2,
}
state.apply()
return state
}
// apply determines the function to use for generating noise, and caches it to reduce overhead
// each time it GetNoise2D or GetNoise3D is invoked.
func (state *State[T]) apply() {
switch state.fractalType {
case FractalFBm:
state.noise2D = genFractalFBM2D[T]
state.noise3D = genFractalFBM3D[T]
case FractalRidged:
state.noise2D = genFractalRidged2D[T]
state.noise3D = genFractalRidged3D[T]
case FractalPingPong:
state.noise2D = genFractalPingPong2D[T]
state.noise3D = genFractalPingPong3D[T]
default:
switch state.noiseType {
case OpenSimplex2:
state.noise2D = singleSimplex2D[T]
state.noise3D = singleOpenSimplex23D[T]
case OpenSimplex2S:
state.noise2D = singleOpenSimplex2S2D[T]
state.noise3D = singleOpenSimplex2S3D[T]
case Cellular:
state.noise2D = singleCellular2D[T]
state.noise3D = singleCellular3D[T]
case Perlin:
state.noise2D = singlePerlin2D[T]
state.noise3D = singlePerlin3D[T]
case ValueCubic:
state.noise2D = singleValueCubic2D[T]
state.noise3D = singleValueCubic3D[T]
case Value:
state.noise2D = singleValue2D[T]
state.noise3D = singleValue3D[T]
default:
state.noise2D = func(_ *State[T], _ int, _, _ T) T { return 0 }
state.noise3D = func(_ *State[T], _ int, _, _, _ T) T { return 0 }
}
}
}
// NoiseType specifies the algorithm that will be used with GetNoise2D and GetNoise3D.
//
// Default: OpenSimplex2
func (state *State[T]) NoiseType(nt NoiseType) {
state.noiseType = nt
state.apply()
}
// FractalType specifies the method used for combining octaves for all fractal noise types.
// Only effects DomainWarp2D and DomainWarp3D functions.
//
// Default: FractalNone
func (state *State[T]) FractalType(ft FractalType) {
state.fractalType = ft
state.apply()
}
// GetNoise2D calculates the noise value at the specified 2D position using the current state
// settings.
//
// This is a convenience function for GetNoise2D that accepts integral coordinates.
// Return values are always normalized and in the range of -1.0 and 1.0.
func (state *State[T]) Noise2D(x, y int) T {
fx, fy := state.transformNoiseCoordinate2D(T(x), T(y))
return state.noise2D(state, state.Seed, fx, fy)
}
// GetNoise3D calculates the noise value at the specified 3D position using the current state
// settings.
//
// This is a convenience function for GetNoise3D that accepts integral coordinates.
// Return values are always normalized and in the range of -1.0 and 1.0.
func (state *State[T]) Noise3D(x, y, z int) T {
fx, fy, fz := state.transformNoiseCoordinate3D(T(x), T(y), T(z))
return state.noise3D(state, state.Seed, fx, fy, fz)
}
// GetNoise2D calculates the noise value at the specified 2D position using the current state
// settings.
//
// Return values are always normalized and in the range of -1.0 and 1.0.
func (state *State[T]) GetNoise2D(x, y T) T {
x, y = state.transformNoiseCoordinate2D(x, y)
return state.noise2D(state, state.Seed, x, y)
}
// GetNoise3D calculates the noise value at the specified 3D position using the current state
// settings.
//
// Return values are always normalized and in the range of -1.0 and 1.0.
func (state *State[T]) GetNoise3D(x, y, z T) T {
x, y, z = state.transformNoiseCoordinate3D(x, y, z)
return state.noise3D(state, state.Seed, x, y, z)
}
// DomainWarp2D warps the input position using current domain warp settings.
func (state *State[T]) DomainWarp2D(x, y T) (T, T) {
xx := x
yy := y
switch state.fractalType {
default:
domainWarpSingle2D(state, &xx, &yy)
case FractalDomainWarpProgressive:
domainWarpFractalProgressive2D(state, &xx, &yy)
case FractalDomainWarpIndependent:
domainWarpFractalIndependent2D(state, &xx, &yy)
}
return xx, yy
}
// DomainWarp2D warps the input position using current domain warp settings.
func (state *State[T]) DomainWarp3D(x, y, z T) (T, T, T) {
xx := x
yy := y
zz := z
switch state.fractalType {
default:
domainWarpSingle3D(state, &xx, &yy, &zz)
case FractalDomainWarpProgressive:
domainWarpFractalProgressive3D(state, &xx, &yy, &zz)
case FractalDomainWarpIndependent:
domainWarpFractalIndependent3D(state, &xx, &yy, &zz)
}
return xx, yy, zz
}
// ====================
// Private/implemenation
// ====================
// Utilities
func fastMin[T Float](x, y T) T {
if x < y {
return x
}
return y
}
func fastMax[T Float](x, y T) T {
if x > y {
return x
}
return y
}
func fastAbs[T Float](f T) T {
if f < 0 {
return -f
}
return f
}
func fastSqrt[T Float](a T) T {
// Benchmarks using Quake's famous "inverse square root" were actually slightly slower than
// using the built-in math library.
return T(math.Sqrt(float64(a)))
}
func fastFloor[T Float](f T) int {
if f >= 0 {
return int(f)
}
return int(f) - 1
}
func fastRound[T Float](f T) int {
if f >= 0 {
return int(f + 0.5)
}
return int(f - 0.5)
}
func lerp[T Float](a, b, t T) T {
return a + t*(b-a)
}
func interpHermite[T Float](t T) T {
return t * t * (3 - 2*t)
}
func interpQuintic[T Float](t T) T {
return t * t * t * (t*(t*6-15) + 10)
}
func cubicLerp[T Float](a, b, c, d, t T) T {
var p T = (d - c) - (a - b)
return t*t*t*p + t*t*((a-b)-p) + t*(c-a) + b
}
func pingPong[T Float](t T) T {
t -= T(int(t*0.5)) * 2
if t < 1 {
return t
}
return 2 - t
}
func calculateFractalBounding[T Float](state *State[T]) T {
gain := fastAbs(state.Gain)
amp := gain
var ampFractal T = 1.0
for i := 1; i < state.Octaves; i++ {
ampFractal += amp
amp *= gain
}
return 1.0 / ampFractal
}
// Hashing
const (
primeX int = 501125321
primeY int = 1136930381
primeZ int = 1720413743
primeX2 = primeX << 1
primeY2 = -2021106534
primeZ2 = -854139810
)
func hash2D(seed, xPrimed, yPrimed int) uint32 {
hash := seed ^ xPrimed ^ yPrimed
return uint32(hash) * 0x27d4eb2d
}
func hash3D(seed, xPrimed, yPrimed, zPrimed int) uint32 {
hash := seed ^ xPrimed ^ yPrimed ^ zPrimed
return uint32(hash) * 0x27d4eb2d
}
func valCoord2D[T Float](seed, xPrimed, yPrimed int) T {
hash := hash2D(seed, xPrimed, yPrimed)
hash *= hash
hash ^= hash << 19
return T(int32(hash)) * (1 / 2147483648.0)
}
func valCoord3D[T Float](seed, xPrimed, yPrimed, zPrimed int) T {
hash := hash3D(seed, xPrimed, yPrimed, zPrimed)
hash *= hash
hash ^= hash << 19
return T(int32(hash)) * (1 / 2147483648.0)
}
func gradCoord2D[T Float](seed, xPrimed, yPrimed int, xd, yd T) T {
hash := hash2D(seed, xPrimed, yPrimed)
hash ^= hash >> 15
hash &= 127 << 1
return xd*T(gradients2D[hash]) + yd*T(gradients2D[hash|1])
}
func gradCoord3D[T Float](seed, xPrimed, yPrimed, zPrimed int, xd, yd, zd T) T {
hash := hash3D(seed, xPrimed, yPrimed, zPrimed)
hash ^= hash >> 15
hash &= 63 << 2
return xd*T(gradients3D[hash]) + yd*T(gradients3D[hash|1]) + zd*T(gradients3D[hash|2])
}
func gradCoordOut2D[T Float](seed, xPrimed, yPrimed int, xo, yo *T) {
hash := hash2D(seed, xPrimed, yPrimed) & (255 << 1)
*xo = T(randVecs2D[hash])
*yo = T(randVecs2D[hash|1])
}
func gradCoordOut3D[T Float](seed, xPrimed, yPrimed, zPrimed int, xo, yo, zo *T) {
hash := hash3D(seed, xPrimed, yPrimed, zPrimed) & (255 << 2)
*xo = T(randVecs3D[hash])
*yo = T(randVecs3D[hash|1])
*zo = T(randVecs3D[hash|2])
}
func gradCoordDual2D[T Float](seed, xPrimed, yPrimed int, xd, yd T, xo, yo *T) {
hash := hash2D(seed, xPrimed, yPrimed)
index1 := hash & (127 << 1)
index2 := (hash >> 7) & (255 << 1)
xg := T(gradients2D[index1])
yg := T(gradients2D[index1|1])
value := xd*xg + yd*yg
xgo := T(randVecs2D[index2])
ygo := T(randVecs2D[index2|1])
*xo = value * xgo
*yo = value * ygo
}
func gradCoordDual3D[T Float](seed, xPrimed, yPrimed, zPrimed int, xd, yd, zd T, xo, yo, zo *T) {
hash := hash3D(seed, xPrimed, yPrimed, zPrimed)
index1 := hash & (63 << 2)
index2 := (hash >> 6) & (255 << 2)
xg := T(gradients3D[index1])
yg := T(gradients3D[index1|1])
zg := T(gradients3D[index1|2])
value := xd*xg + yd*yg + zd*zg
xgo := T(randVecs3D[index2])
ygo := T(randVecs3D[index2|1])
zgo := T(randVecs3D[index2|2])
*xo = value * xgo
*yo = value * ygo
*zo = value * zgo
}
func genNoiseSingle2D[T Float](state *State[T], seed int, x, y T) T {
switch state.noiseType {
case OpenSimplex2:
return singleSimplex2D(state, seed, x, y)
case OpenSimplex2S:
return singleOpenSimplex2S2D(state, seed, x, y)
case Cellular:
return singleCellular2D(state, seed, x, y)
case Perlin:
return singlePerlin2D(state, seed, x, y)
case ValueCubic:
return singleValueCubic2D(state, seed, x, y)
case Value:
return singleValue2D(state, seed, x, y)