diff --git a/main.lua b/main.lua
index 312d0ae..874f979 100644
--- a/main.lua
+++ b/main.lua
@@ -11,12 +11,13 @@ local function rng()
     local r = love.math.newRandomGenerator(1)
     return function() return r:random() end
 end
-local n1,g1 = Noise.make1d(8,rng(),decay)
-local n2,g2 = Noise.make2d(9,rng(),decay)
-local n3,g3 = Noise.make3d(11,rng(),decay)
-local s1,s1g = Noise.make1dShader(9,rng(),decay)
-local s2,s2g = Noise.make2dShader(13,rng(),decay)
-local s3,s3g = Noise.make3dShader(17,rng(),decay)
+local makeAmps = Noise.makeAmplitudes
+local n1,g1 = Noise.make1d(makeAmps(8, decay), rng())
+local n2,g2 = Noise.make2d(makeAmps(9, decay), rng())
+local n3,g3 = Noise.make3d(makeAmps(11, decay), rng())
+local s1,s1g = Noise.make1dShader(makeAmps(9, decay), rng())
+local s2,s2g = Noise.make2dShader(makeAmps(13, decay), rng())
+local s3,s3g = Noise.make3dShader(makeAmps(17, decay), rng())
 
 local cw,ch = W/2,H/3
 local canv = lg.newCanvas(cw,ch)
diff --git a/noise.lua b/noise.lua
index f2eaf3d..e889221 100644
--- a/noise.lua
+++ b/noise.lua
@@ -10,37 +10,44 @@ local function cdf_prime(x, dx)
     return (0.31831 * exp(-2/PI * x*x) * abs(x)*dx)/sqrt(1-exp(-2/PI*x*x))
 end
 
-local function _defaultArgs(resolution,random,decayFn)
-    if not resolution then resolution = 4 end
+local function _defaultArgs(amplitudes,random)
+    if amplitudes == nil then amplitudes = 5 end
+    if type(amplitudes) == 'number' then
+        amplitudes = noise.makeAmplitudes(amplitudes, function(x) return .1^x end)
+    end
     if not random then random = math.random end
-    if not decayFn then decayFn = function(x) return .1^x end end
-    return resolution,random,decayFn
+    return amplitudes, random
 end
 
-local function _amplitudesAndOffsets(decayFn,numAmplitudes, numOffsets, random)
+local function calculateSigma(amplitudes)
     local sigma = 0
-    local amplitudes = {}
-    for i=1,numAmplitudes do
-        local a = decayFn((i-1+random())/numAmplitudes)
-        amplitudes[i] = a
-        assert(a > 0.0001)
-        sigma = sigma + a^2
+    for _,a in ipairs(amplitudes) do
+        sigma = sigma + a*a
     end
-    sigma = math.sqrt(sigma/2)
+    return math.sqrt(sigma/2)
+end
+
+local function makeOffsets(count, random)
     local offsets = {}
-    for i=1,numOffsets do
+    for i=1,count do
         offsets[i] = random()*TAU
     end
-    return amplitudes,sigma,offsets
+    return offsets
 end
 
-local function sign(x)
-    if x == 0 then return 0
-    elseif x < 0 then return -1 else return 1 end
+noise.makeAmplitudes = function(count, fn)
+    local amplitudes = {}
+    for i=1,count do
+        amplitudes[i] = fn((i-.5)/count)
+    end
+    return amplitudes
 end
-noise.make1d = function(resolution,random,decayFn)
-    resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
-    local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,resolution,random)
+
+noise.make1d = function(amplitudes,random)
+    amplitudes, random = _defaultArgs(amplitudes, random)
+    local resolution = #amplitudes
+    local sigma = calculateSigma(amplitudes)
+    local offsets = makeOffsets(#amplitudes, random)
     local function noise(x)
         local n = 0
         for i,a in ipairs(amplitudes) do
@@ -63,9 +70,11 @@ noise.make1d = function(resolution,random,decayFn)
     return noise, gradient
 end
 
-noise.make2d = function(resolution,random,decayFn)
-    resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
-    local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,2*resolution,random)
+noise.make2d = function(amplitudes, random)
+    amplitudes, random = _defaultArgs(amplitudes, random)
+    local resolution = #amplitudes
+    local sigma = calculateSigma(amplitudes)
+    local offsets = makeOffsets(2*#amplitudes, random)
     sigma = sigma/sqrt(2)
     local function noise(x,y)
         local n = 0
@@ -100,9 +109,11 @@ noise.make2d = function(resolution,random,decayFn)
     return noise, gradient
 end
 
-noise.make3d = function(resolution,random,decayFn)
-    resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
-    local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,3*resolution,random)
+noise.make3d = function(amplitudes, random)
+    amplitudes, random = _defaultArgs(amplitudes, random)
+    local resolution = #amplitudes
+    local sigma = calculateSigma(amplitudes)
+    local offsets = makeOffsets(3*#amplitudes, random)
     sigma = sigma/sqrt(3)
     local function noise(x,y,z)
         -- Find the biggest fibonacci number F_n such that F_n < resolution
@@ -228,15 +239,14 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
 }
 ]]
 
-noise.make1dShader = function(resolution,random,decayFn)
-    resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
-    if type(resolution) ~= 'number' or (resolution % 1 > 0) or (resolution <= 0) then
-        error("Resolution must be a positive integer.")
-    end
+noise.make1dShader = function(amplitudes, random)
+    amplitudes, random = _defaultArgs(amplitudes, random)
+    local resolution = #amplitudes
+    local sigma = calculateSigma(amplitudes)
+    local offsets = makeOffsets(#amplitudes, random)
     local shaderCode = "#define RESOLUTION "..tostring(resolution).."\n"..shader1d
     local noiseShader = lg.newShader(shaderCode)
     local gradShader = lg.newShader("#define GRADIENT\n"..shaderCode)
-    local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,resolution,random)
     do -- Dumb hack to work around a bug in Love 0.10.2 not sending the last value
         table.insert(amplitudes, 1.)
         table.insert(offsets, 1.)
@@ -299,15 +309,14 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
 }
 ]]
 
-noise.make2dShader = function(resolution,random,decayFn)
-    resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
-    if type(resolution) ~= 'number' or (resolution % 1 > 0) or (resolution <= 0) then
-        error("Resolution must be a positive integer.")
-    end
+noise.make2dShader = function(amplitudes, random)
+    amplitudes, random = _defaultArgs(amplitudes, random)
+    local resolution = #amplitudes
+    local sigma = calculateSigma(amplitudes)
+    local offsets = makeOffsets(2*#amplitudes, random)
     local shaderCode = "#define RESOLUTION "..tostring(resolution).."\n"..shader2d
     local noiseShader = lg.newShader(shaderCode)
     local gradShader = lg.newShader("#define GRADIENT\n"..shaderCode)
-    local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,2*resolution,random)
     sigma = sigma/sqrt(2)
     local offsets2 = {}
     for i=1,#offsets-1,2 do
@@ -405,15 +414,14 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
 }
 ]]
 
-noise.make3dShader = function(resolution,random,decayFn)
-    resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
-    if type(resolution) ~= 'number' or (resolution % 1 > 0) or (resolution <= 0) then
-        error("Resolution must be a positive integer.")
-    end
+noise.make3dShader = function(amplitudes, random)
+    amplitudes, random = _defaultArgs(amplitudes, random)
+    local resolution = #amplitudes
+    local sigma = calculateSigma(amplitudes)
+    local offsets = makeOffsets(3*#amplitudes, random)
     local shaderCode = "#define RESOLUTION "..tostring(resolution).."\n"..shader3d
     local noiseShader = lg.newShader(shaderCode)
     local gradShader = lg.newShader("#define GRADIENT\n"..shaderCode)
-    local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,3*resolution,random)
     sigma = sigma/sqrt(3)
     local offsets2 = {}
     for i=1,#offsets-1,3 do