From af65f8412885b96dd1bcb30b952be72c9aaa526e Mon Sep 17 00:00:00 2001
From: shoofle <xsigma@gmail.com>
Date: Tue, 10 Sep 2013 14:05:50 -0400
Subject: [PATCH] Working on a fourth engine type.

---
 .../dynamic_systems_in_games.article.html     | 30 ++++++++++++++-----
 1 file changed, 23 insertions(+), 7 deletions(-)

diff --git a/articles/dynamic_systems_in_games.article.html b/articles/dynamic_systems_in_games.article.html
index 89a6f20..f5941e3 100644
--- a/articles/dynamic_systems_in_games.article.html
+++ b/articles/dynamic_systems_in_games.article.html
@@ -68,14 +68,17 @@
 <div class="row-fluid">
 	<div id="fuel-management-3" class="span4 offset4">
 		<script type="text/javascript">
-			var f, t;
+			var gaussian = function (x) { return Math.exp(-x*x); };
+			var dgauss = function (x) { return x * gaussian(x); };
+			var recenter = function (fn, center, scale) { return function (x) { return fn( (x-center)/scale ); }; };
+
 			var e3=engine($('#fuel-management-3'), function (sq) {
 				if (sq.temperature.value < sq.ignition_threshhold.value) {
 					return 0;
 				}
-				f = 10*sq.fuel_flow_rate.value;
-				t = sq.temperature.value - f - sq.ignition_threshhold.value;
-				return 5 * (t/Math.sqrt(f)) * Math.exp(-t*t/(f));
+				return 5*recenter(dgauss, 
+					10*sq.fuel_flow_rate.value + sq.ignition_threshhold.value, 
+					Math.sqrt(10*sq.fuel_flow_rate.value)) (sq.temperature.value);
 			});
 		</script>
 		<div class="flow_rate">
@@ -89,15 +92,28 @@
 		<div class="potential_plot" style="width:100%;height:300px"></div>
 	</div>
 </div>
+<p>Sweet! That's very much what I'm going for, at least in the peak. For the time being, I'm not worrying about what it's like far outside what we want to be the stable point. Now, though, it takes <em>too much</em> work to keep it stable.</p>
 <div class="row-fluid">
-	<div id="fuel-management-3" class="span4 offset4">
+	<div id="fuel-management-4" class="span4 offset4">
 		<script type="text/javascript">
 			// describe a better potential graph
-			// var e3=engine($('#fuel-management-3'), heyo2);
+			var e4=engine($('#fuel-management-4'), function (sq) {
+				if (sq.temperature.value < sq.ignition_threshhold.value) {
+					return 0;
+				}
+				var y = 0;
+				y += 10*recenter(dgauss, 
+					10*sq.fuel_flow_rate.value + sq.ignition_threshhold.value,
+					Math.sqrt(10*sq.fuel_flow_rate.value)) (sq.temperature.value);
+				y -= 5*recenter(dgauss, 
+					10*sq.fuel_flow_rate.value + sq.ignition_threshhold.value,
+					Math.sqrt(2*sq.fuel_flow_rate.value)) (sq.temperature.value);
+				return y;
+			});
 		</script>
 		<div class="flow_rate">
 			<label for="fuel">Fuel Flow Rate</label>
-			<input type="range" name="fuel" min=0 max=0.25 step=0.001 value=0.1>
+			<input type="range" name="fuel" min=0 max=1 step=0.001 value=0.1>
 		</div>
 		<input type="button" name="ignition" value="Ignite!">
 		<span><span class="temp-out">0</span> degrees</span>