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elevator_paradox.html
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elevator_paradox.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>Elevator Paradox</title>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,300italic,700,700italic">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/normalize/3.0.3/normalize.css">
<link rel="stylesheet" href="css/milligram.min.css">
<link rel="stylesheet" href="css/mrwojo.css">
<script src="d3/d3.min.js" charset="utf-8"></script>
</head>
<body>
<main>
<div id="content">
<h1>Elevator paradox, racetrack visualization</h1>
<p>From Wikipedia "<a href="https://en.wikipedia.org/w/index.php?title=Elevator_paradox&oldid=702582011#Modeling_the_elevator_problem">Elevator paradox</a>":</p>
<blockquote>Another visualization [of the elevator paradox] is to imagine sitting in bleachers near one end of an oval racetrack: if you are waiting for a single car to pass in front of you, it will be more likely to pass on the straight-away before entering the turn.</blockquote>
<p>This is a visualization of what I believe was meant by this statement.</p>
<p>Below is an oval racetrack with a single racecar going around. The eyes represent "you". The cyan line represents "in front of you". The eyes look at the track at random times, and then they wait for the racecar to pass in front. Most of the time, the racecar will pass in the direction of entering the turn, similar to the other examples of the elevator paradox.</p>
<svg id="stadium" width="600" height="300"></svg>
<table>
<tr>
<td>Times entering the turn</td>
<td><span id="cross-in">0</span></td>
</tr>
<tr>
<td>Times exiting the turn</td>
<td><span id="cross-out">0</span></td>
</tr>
</table>
</div>
<footer>
<p>Mark Wojtowicz</p>
</footer>
</main>
<script type="text/javascript">
// TODO: canvas size, track size all dependent
// A car that appears on the track.
var Car = function() {
this.position = Math.random();
this.speed = 0.25; // in revolutions per sec
// updates car position
this.update = function(dt) {
this.position += this.speed * dt;
// circular
if (this.position > 1) {
this.position -= 1;
}
};
};
var track = {
// track center position
cx: 300,
cy: 150,
// oval track semimajor/semiminor axes
majorRadius: 280,
minorRadius: 120,
// converts position t in range [0 1) to pixel coordinates on track
parametricPosition: function(t) {
return {
x: track.cx + track.majorRadius * Math.cos(2 * Math.PI * t),
y: track.cy + track.minorRadius * Math.sin(2 * Math.PI * t)
}
}
};
var sim = {
// delta time (per frame)
dt: 1 / 15,
// frame count
frame: 0,
// initialize the simulation
init: function() {
var stadiumElem = d3.select("#stadium");
// show track
var trackOval = stadiumElem.append("ellipse")
.attr("cx", track.cx)
.attr("cy", track.cy)
.attr("rx", track.majorRadius)
.attr("ry", track.minorRadius)
.attr("style", "fill:#567714;stroke:black;stroke-width:14");
// show eye position
var eyeGroup = stadiumElem.append("g").attr("id", "eye");
var eyeSymbol = eyeGroup.append("text")
.attr("x", sim.eyeX)
.attr("y", sim.eyeY)
.attr("text-anchor", "middle")
.attr("id", sim.eyeY)
.text("👀");
var eyeLine = eyeGroup.append("line")
.attr("x1", sim.eyeX)
.attr("y1", sim.eyeY)
.attr("x2", sim.eyeX)
.attr("y2", 300)
.attr("style", "stroke:#00F0FF;stroke-width:4;stroke-dasharray:4");
sim.activateEyes(false);
// create the cars
var n_cars = 1;
sim.cars = new Array();
for (var i = 0; i < n_cars; i++) {
sim.cars.push(new Car());
// circles represent cars
var pos = track.parametricPosition(sim.cars[i].position);
stadiumElem.append("circle")
.attr("cx", pos.x)
.attr("cy", pos.y)
.attr("r", 5)
.attr("style", "fill:none;stroke:orange;stroke-width:3")
.attr("class", "car");
}
},
// is the viewer currently active?
eyeActive: false,
// viewer coordinates
eyeX: 500,
eyeY: 40,
// enable/disable the viewer
activateEyes: function(show) {
var eyes = d3.select("#eye");
sim.eyeActive = show;
if (show) {
eyes.attr("style", "opacity:1");
} else {
eyes.attr("style", "opacity:0.25");
}
},
// count the number of times the viewer sees the car entering, exiting the turn
carEnters: 0,
carExits: 0,
_updateCount: function() {
// originally had a chart, the numbers are just fine
d3.select("#cross-in").text(sim.carEnters);
d3.select("#cross-out").text(sim.carExits);
},
// called when viewer sees a car entering the turn
carEntered: function() {
sim.carEnters += 1;
sim._updateCount();
},
// called when viewer sees a car exiting the turn
carExited: function() {
sim.carExits += 1;
sim._updateCount();
},
// step the simulation
update: function() {
sim.frame += 1;
var carElems = d3.selectAll("#stadium .car")[0];
for (var i = 0; i < sim.cars.length; i++) {
var oldX = carElems[i].attributes.cx.value;
sim.cars[i].update(sim.dt);
// move cars on the track
pos = track.parametricPosition(sim.cars[i].position);
carElems[i].setAttribute("cx", pos.x);
carElems[i].setAttribute("cy", pos.y);
// did this car cross the viewer's eye line?
if (sim.eyeActive) {
if (oldX <= sim.eyeX && pos.x > sim.eyeX) {
sim.carEntered();
sim.activateEyes(false);
} else if (oldX >= sim.eyeX && pos.x < sim.eyeX) {
sim.carExited();
sim.activateEyes(false);
}
}
}
// Activate the viewer at random times.
if (Math.random() < (sim.dt / 2)) {
sim.activateEyes(true);
}
// Stop the simulation after a while.
if (sim.frame > 10000) {
clearInterval(sim._interval);
}
}
};
sim.init();
sim._interval = setInterval(sim.update, sim.dt * 1000);
</script>
</body>
</html>