diff --git a/conf.lua b/demo/conf.lua
similarity index 100%
rename from conf.lua
rename to demo/conf.lua
diff --git a/histogram.lua b/demo/histogram.lua
similarity index 100%
rename from histogram.lua
rename to demo/histogram.lua
diff --git a/main.lua b/demo/main.lua
similarity index 97%
rename from main.lua
rename to demo/main.lua
index a53008d..aa5bb6b 100644
--- a/main.lua
+++ b/demo/main.lua
@@ -1,5 +1,7 @@
-local Histogram = require 'histogram'
+-- Update the package path because noise.lua is in the parent directory:
+package.path = package.path .. ";../noise.lua"
 local Noise = require "noise"
+local Histogram = require 'histogram'
 local DRAW_RES = love.window.toPixels(4)
 local SCALE = 100
 
@@ -8,6 +10,8 @@ local n1,g1 = Noise.make1d{resolution=5, distribution=decay, seed=1}
 local n2,g2 = Noise.make2d{resolution=7, distribution=decay, seed=1}
 local n3,g3 = Noise.make3d{resolution=9, distribution=decay, seed=1}
 local s1,s1g = Noise.make1dShader{resolution=10, distribution=decay, seed=1}
+s1:send("draw_outline",true)
+s1g:send("draw_outline",true)
 local s2,s2g = Noise.make2dShader{resolution=15, distribution=decay, seed=1}
 local s3,s3g = Noise.make3dShader{resolution=20, distribution=decay, seed=1}
 
diff --git a/noise.lua b/noise.lua
index f5ecfd3..44fdd0d 100644
--- a/noise.lua
+++ b/noise.lua
@@ -38,8 +38,15 @@
 --     love.graphics.setShader(noise_shader)
 --     love.graphics.draw(canvas)
 --     love.graphics.setShader()
--- The noise gradient shaders populate the RGB channels with dn/dx, dn/dy, dn/dz partial
--- derivatives, where [-1,0,1] is remapped to [0,0.5,1]. 
+-- The noise gradient shaders populate the RGB channels with:
+--   * for 1D: sigmoid(2*dn/dx), sigmoid(2*dn/dx), sigmoid(2*dn/dx)
+--   * for 2D: sigmoid(1.5*dn/dx), sigmoid(1.5*dn/dy), 0
+--   * for 3D: sigmoid(4*dn/dx), sigmoid(4*dn/dy), sigmoid(4*dn/dz)
+-- (coefficients were arbitrarily chosen to best squash typical gradients for the default
+--  parameters evenly into (0,1))
+-- Additionally, the 1D noise shader has an extra variable "draw_outline" that, if set to
+-- true, makes the 1D shader render output as white or black if the y-coordinate is
+-- above/below the  noise value for a given x-coordinate.
 -- 
 -- 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
@@ -274,10 +281,14 @@ if love and love.graphics then
     local shader1d = [[
     #define TAU 6.283185307179586476925286766559005768394338798750211641949
     #define MAX_RESOLUTION 64
+    #define SIGMOID(x) (1./(1.+exp(-(x))))
+    #define CDF(x) (.5 + .5*sign(x)*sqrt(1.-exp(-4./TAU * (x)*(x))))
+    #define CDF_PRIME(x, dx) ((0.31831 * exp(-4./TAU * (x)*(x)) * abs(x)*(dx))/sqrt(1.0-exp(-4./TAU * (x)*(x))))
     extern int resolution;
     extern float sigma, range_min, range_max;
     extern float amplitudes[MAX_RESOLUTION];
     extern float offsets[MAX_RESOLUTION];
+    extern bool draw_outline = false;
 
     vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
     {
@@ -295,14 +306,20 @@ if love and love.graphics then
         }
         noise /= sigma;
     #ifdef GRADIENT
-        dndx /= sigma;
-        dndx = (0.31831 * exp(-4./TAU * noise*noise) * abs(noise)*dndx)/sqrt(1.0-exp(-4./TAU * noise*noise));
-        // TODO: normalize properly
-        dndx = .5 + .5*dndx;
-        return vec4(dndx,dndx,dndx, 1.);
+        dndx = CDF_PRIME(noise, dndx/sigma);
+        dndx = SIGMOID(dndx*2.);
+        if (draw_outline) {
+            return texture_coords.y > (1.-dndx) ? vec4(1.,1.,1.,1.) : vec4(0.,0.,0.,1.);
+        } else {
+            return vec4(dndx,dndx,dndx,1.);
+        }
     #else
-        noise = .5 + .5*sign(noise)*sqrt(1.-exp(-4./TAU * noise*noise));
-        return vec4(noise,noise,noise, 1.);
+        noise = CDF(noise);
+        if (draw_outline) {
+            return texture_coords.y > (1.-noise) ? vec4(1.,1.,1.,1.) : vec4(0.,0.,0.,1.);
+        } else {
+            return vec4(noise,noise,noise,1.);
+        }
     #endif
     }
     ]]
@@ -333,6 +350,9 @@ if love and love.graphics then
     local shader2d = [[
     #define TAU 6.283185307179586476925286766559005768394338798750211641949
     #define PHI 1.618033988749894848204586834365638117720309179805762862135
+    #define CDF(x) (.5 + .5*sign(x)*sqrt(1.-exp(-4./TAU * (x)*(x))))
+    #define CDF_PRIME(x, dx) ((0.31831 * exp(-4./TAU * (x)*(x)) * abs(x)*(dx))/sqrt(1.0-exp(-4./TAU * (x)*(x))))
+    #define SIGMOID(x) (1./(1.+exp(-2.*(x))))
     extern float sigma;
     extern float amplitudes[RESOLUTION];
     extern vec2 offsets[RESOLUTION];
@@ -358,20 +378,19 @@ if love and love.graphics then
             dndy += sina*sin(u/a + k) + cosa*sin(v/a + w);
     #endif
         }
-        noise /= 2.*sigma;
 
+        float _sigma = 2.*sigma;
+        noise /= _sigma;
     #ifdef GRADIENT
-        dndx /= 2.*sigma;
-        dndx = (0.31831 * exp(-4./TAU * noise*noise) * abs(noise)*dndx)/sqrt(1.0-exp(-4./TAU * noise*noise));
-        dndx = .5 + .5*dndx;
+        dndx = CDF_PRIME(noise, dndx/_sigma);
+        dndx = SIGMOID(dndx*1.5);
 
-        dndy /= 2.*sigma;
-        dndy = (0.31831 * exp(-4./TAU * noise*noise) * abs(noise)*dndy)/sqrt(1.0-exp(-4./TAU * noise*noise));
-        dndy = .5 + .5*dndy;
+        dndy = CDF_PRIME(noise, dndy/_sigma);
+        dndy = SIGMOID(dndy*1.5);
 
         return vec4(dndx,dndy,0.,1.);
     #else
-        noise = .5 + .5*sign(noise)*sqrt(1.-exp(-4./TAU * noise*noise));
+        noise = CDF(noise);
         return vec4(noise,noise,noise,1.);
     #endif
     }
@@ -409,6 +428,9 @@ if love and love.graphics then
     #define PHI 1.618033988749894848204586834365638117720309179805762862135
     #define LOG_PHI 0.481211825059603447497758913424368423135184334385660519660
     #define SQRT5 2.236067977499789696409173668731276235440618359611525724270
+    #define CDF(x) (.5 + .5*sign(x)*sqrt(1.-exp(-4./TAU * (x)*(x))))
+    #define CDF_PRIME(x, dx) ((0.31831 * exp(-4./TAU * (x)*(x)) * abs(x)*(dx))/sqrt(1.0-exp(-4./TAU * (x)*(x))))
+    #define SIGMOID(x) (1./(1.+exp(-2.*(x))))
     extern float sigma, z;
     extern float amplitudes[RESOLUTION];
     extern vec3 offsets[RESOLUTION];
@@ -460,23 +482,21 @@ if love and love.graphics then
             dndz += (n1.z*k.x + n2.z*k.y + n3.z*k.z)/3.;
     #endif
         }
-        n /= 3.*sigma;
+        float _sigma = 3.*sigma;
+        n /= _sigma;
     #ifdef GRADIENT
-        dndx /= sigma;
-        dndx = (0.31831 * exp(-4./TAU * n*n) * abs(n)*dndx)/sqrt(1.0-exp(-4./TAU * n*n));
-        dndx = .5 + .5*dndx;
+        dndx = CDF_PRIME(n, dndx/_sigma);
+        dndx = SIGMOID(dndx*4.);
 
-        dndy /= sigma;
-        dndy = (0.31831 * exp(-4./TAU * n*n) * abs(n)*dndy)/sqrt(1.0-exp(-4./TAU * n*n));
-        dndy = .5 + .5*dndy;
+        dndy = CDF_PRIME(n, dndy/_sigma);
+        dndy = SIGMOID(dndy*4.);
 
-        dndz /= sigma;
-        dndz = (0.31831 * exp(-4./TAU * n*n) * abs(n)*dndz)/sqrt(1.0-exp(-4./TAU * n*n));
-        dndz = .5 + .5*dndz;
+        dndz = CDF_PRIME(n, dndz);
+        dndz = SIGMOID(dndz*4.);
 
         return vec4(dndx,dndy,dndz, 1.);
     #else
-        n = .5 + .5*sign(n)*sqrt(1.-exp(-4./TAU * n*n));
+        n = CDF(n);
         return vec4(n,n,n,1.);
     #endif
     }
diff --git a/noise1d.glsl b/noise1d.glsl
index 84af06b..9d5fd81 100644
--- a/noise1d.glsl
+++ b/noise1d.glsl
@@ -5,6 +5,7 @@ extern float sigma;
 extern float amplitudes[MAX_RESOLUTION];
 extern float offsets[MAX_RESOLUTION];
 extern float range_min, range_max;
+extern bool draw_outline = false;
 
 float cdf(float x) {
     return .5 + .5*sign(x)*sqrt(1.-exp(-4./TAU * x*x));
@@ -23,6 +24,9 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
 {
     float x = mix(range_min,range_max,texture_coords.x);
     float n = noise1d(x);
-    //return vec4(n,n,n,1.);
-    return texture_coords.y > (1.-n) ? vec4(1.,1.,1.,1.) : vec4(0.,0.,0.,1.);
+    if (draw_outline) {
+        return texture_coords.y > (1.-n) ? vec4(1.,1.,1.,1.) : vec4(0.,0.,0.,1.);
+    } else {
+        return vec4(n,n,n,1.);
+    }
 }