Line Circle Illusion

.block

license: mit
height: 540
border: no

README.md

Line Circle Illusion

I saw a pretty cool post on reddit the other day and I thought it would be fun to recreate it using canvas and D3. Here it is!

dist.js

function colorScale(e){return rawColorScale(colorScaleMapper(e))}function createCircles(){for(var e=[],t=0;t<=maxCirclePower;t++)e=e.concat(createCirclePower(t));return e}function createCirclePower(e){var t=Math.pow(2,e),r=Math.pow(2,Math.max(0,e-1)),a=d3.range(r).map(function(e){var r=angleScale((2*e+1)/t);return createCircle(r)});return a}function createCircle(e){var t=.5,r=positionScale(e),a=t*Math.cos(e)+t,o=t*Math.sin(e)+t,c=t*Math.cos(e+Math.PI)+t,i=t*Math.sin(e+Math.PI)+t,l=d3.easeQuad(r),n=(1-l)*a+l*c,s=(1-l)*o+l*i;return{tPosition:r,direction:1,color:3*r,x:n,y:s,sx:a,sy:o,tx:c,ty:i}}function draw(e){ctx.save();for(var t,r=0;r<e.length&&r<numCirclesToShow;++r)t=e[r],ctx.beginPath(),ctx.arc(xScale(t.x),yScale(t.y),radius,0,tau),ctx.fillStyle=colorScale(t.color),ctx.fill(),ctx.closePath();ctx.restore()}function update(e){for(var t,r=0;r<e.length;++r){t=e[r],t.tPosition=Math.max(0,Math.min(t.tPosition+tickAmount*t.direction,1)),1!==t.tPosition&&0!==t.tPosition||(t.direction*=-1);var a=d3.easeQuad(t.tPosition);t.x=(1-a)*t.sx+a*t.tx,t.y=(1-a)*t.sy+a*t.ty,t.color=t.color+tickAmount,t.color+1e-6>3&&(t.color=0)}}function updateConfig(){radius=+d3.select("#radius").node().value,plotAreaWidth=width-2*radius,plotAreaHeight=height-2*radius,xScale.range([0,plotAreaWidth]),yScale.range([0,plotAreaHeight]),tickAmount=+d3.select("#tickAmount").node().value,colorInterpolator=d3[d3.select("#colorInterpolator").node().value],rawColorScale.interpolator(colorInterpolator),ctx.restore(),ctx.save(),ctx.translate(radius,radius),ctx.clearRect(-radius,-radius,width,height)}var tau=2*Math.PI,width=400,height=400,radius=10,plotAreaWidth=width-2*radius,plotAreaHeight=height-2*radius,tickAmount=.01,maxCirclePower=9,circlePower=0,numCirclesToShow=Math.pow(2,circlePower),numLoopsAtMax=4,resetCountdown=numLoopsAtMax,colorInterpolator=d3.interpolateRainbow,screenScale=window.devicePixelRatio||1,canvas=d3.select("canvas").attr("width",width*screenScale).attr("height",height*screenScale).style("width",width+"px").style("height",height+"px"),ctx=canvas.node().getContext("2d");ctx.scale(screenScale,screenScale),ctx.save(),ctx.translate(radius,radius);var xScale=d3.scaleLinear().domain([0,1]).range([0,plotAreaWidth]),yScale=d3.scaleLinear().domain([0,1]).range([0,plotAreaHeight]),angleScale=d3.scaleLinear().domain([0,1]).range([0,Math.PI]),positionScale=d3.scaleLinear().domain([0,Math.PI]).range([1,0]),colorScaleMapper=d3.scaleLinear().domain([0,1,1.5,2,3]).range([0,.6666666667,1,.666666667,0]),rawColorScale=d3.scaleSequential(colorInterpolator),circles=createCircles();draw(circles);var timer=d3.timer(function(e){update(circles),draw(circles),0===circles[0].tPosition&&(circlePower<maxCirclePower?(circlePower+=1,numCirclesToShow=Math.pow(2,circlePower)):0===resetCountdown?(circlePower=0,numCirclesToShow=Math.pow(2,circlePower),resetCountdown=numLoopsAtMax,ctx.clearRect(-radius,-radius,width,height)):resetCountdown-=1,console.log("Showing "+numCirclesToShow+" circles. Reset Countdown = "+resetCountdown))});d3.select(".controls").selectAll("input, select").on("change",updateConfig);
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2 * radius;\nlet plotAreaHeight = height - 2 * radius;\n\n// corresponds to speed of circles. can be fun to play with.\nlet tickAmount = 0.01;\n\n// we get 2^power number of circles drawn\nconst maxCirclePower = 9;\nlet circlePower = 0;\nlet numCirclesToShow = Math.pow(2, circlePower);\n\n// after we have reached max power, how many loops\n// before resetting to 1 circle?\nconst numLoopsAtMax = 4;\nlet resetCountdown = numLoopsAtMax;\n\n// set the color scheme here:\nlet colorInterpolator = d3.interpolateRainbow;\n\n// create the canvas\nconst screenScale = window.devicePixelRatio || 1;\nconst canvas = d3.select('canvas')\n  .attr('width', width * screenScale)\n  .attr('height', height * screenScale)\n  .style('width', `${width}px`)\n  .style('height', `${height}px`)\nconst ctx = canvas.node().getContext('2d');\nctx.scale(screenScale, screenScale);\nctx.save();\nctx.translate(radius, radius);\n\n// position scales\nconst xScale = d3.scaleLinear().domain([0, 1]).range([0, plotAreaWidth]);\nconst yScale = d3.scaleLinear().domain([0, 1]).range([0, plotAreaHeight]);\nconst angleScale = d3.scaleLinear().domain([0, 1]).range([0, Math.PI]);\nconst positionScale = d3.scaleLinear().domain([0, Math.PI]).range([1, 0])\n\n// colors-- we want to repeat every 3 trips while looping from one end\n// to the other and back to the beginning.\nconst colorScaleMapper = d3.scaleLinear()\n\t.domain([0, 1, 1.5, 2, 3])\n\t.range([0, 0.6666666667, 1, 0.666666667, 0])\n\n// t goes from 0 to 2\nconst rawColorScale = d3.scaleSequential(colorInterpolator);\nfunction colorScale(t) {\n\treturn rawColorScale(colorScaleMapper(t))\n}\n\n\n// create circles by adding in levels based on powers of 2\nfunction createCircles() {\n\tlet circles = [];\n\tfor (let i = 0; i <= maxCirclePower; i++) {\n\t\tcircles = circles.concat(createCirclePower(i));\n\t}\n\n\treturn circles;\n}\n\n/*\n  create circles for a given power of 2.\n  e.g.:\n\tpower=0  1,\n\tpower=1  1/2,\n\tpower=2  1/4 3/4\n\tpower=3  1/8 3/8 5/8 7/8\n\tpower=4  1/16 3/16 5/16 7/16 9/16 11/16\n*/\nfunction createCirclePower(power) {\n\tconst denominator = Math.pow(2, power);\n\tconst numCirclesToAdd = Math.pow(2, Math.max(0, power - 1))\n\n\tconst circleRing = d3.range(numCirclesToAdd).map((i) => {\n\t\tconst angle = angleScale(((2 * i) + 1) / denominator);\n\t\treturn createCircle(angle);\n\t});\n\n\treturn circleRing;\n}\n\n// create a single circle at a given angle\nfunction createCircle(angle) {\n\tconst baseRadius = 0.5;\n\tconst tPosition = positionScale(angle);\n\n\t// use polar coordinates\n\tconst sx = baseRadius * Math.cos(angle) + baseRadius;\n\tconst sy = baseRadius * Math.sin(angle) + baseRadius;\n\tconst tx = baseRadius * Math.cos(angle + Math.PI) + baseRadius;\n\tconst ty = baseRadius * Math.sin(angle + Math.PI) + baseRadius;\n\n\t// linear interpolate with quadratic easing (easing should match update func)\n\tconst t = d3.easeQuad(tPosition);\n\tconst x = (1 - t) * sx + t * tx;\n\tconst y = (1 - t) * sy + t * ty;\n\n\treturn {\n\t\ttPosition,\n\t\tdirection: 1,\n\t\tcolor: tPosition * 3,\n\t\tx,\n\t\ty,\n\t\tsx,\n\t\tsy,\n\t\ttx,\n\t\tty,\n\t};\n}\n\n// draw circles on screen\nfunction draw(circles) {\n\tctx.save();\n\n\tlet circle;\n\tfor (let i = 0; i < circles.length && i < numCirclesToShow; ++i) {\n\t\tcircle = circles[i];\n\t\tctx.beginPath();\n\t\tctx.arc(xScale(circle.x), yScale(circle.y), radius, 0, tau)\n\t\tctx.fillStyle = colorScale(circle.color);\n\t\tctx.fill()\n\t\tctx.closePath();\n\t}\n\n\tctx.restore();\n}\n\n// update circle positions\nfunction update(circles) {\n\tlet circle;\n\tfor (let i = 0; i < circles.length; ++i) {\n\t\tcircle = circles[i];\n\n\t\t// update position\n\t\tcircle.tPosition = Math.max(0, Math.min(circle.tPosition + tickAmount * circle.direction, 1));\n\t\tif (circle.tPosition === 1 || circle.tPosition === 0) {\n\t\t\tcircle.direction *= -1;\n\t\t}\n\n\t\t// important to use quadratic easing to get the circle illusion shape\n\t\tconst t = d3.easeQuad(circle.tPosition);\n\t\tcircle.x = (1 - t) * circle.sx + t * circle.tx;\n\t\tcircle.y = (1 - t) * circle.sy + t * circle.ty;\n\n\t\t// update color\n\t\tcircle.color = circle.color + tickAmount;\n\n\t\t// fix rounding error\n\t\tif (circle.color + 1e-6 > 3) {\n\t\t\tcircle.color = 0;\n\t\t}\n\t}\n}\n\n\n// create the circles and draw them\nconst circles = createCircles();\ndraw(circles);\n\n// begin a timer for doubling the number of circles at regular intervals\nlet timer = d3.timer((elapsed) => {\n\tupdate(circles);\n\tdraw(circles);\n\n\t// if the first circle is back in start position, add a new ring\n\tif (circles[0].tPosition === 0) {\n\t\tif (circlePower < maxCirclePower) {\n\t\t\tcirclePower += 1;\n\t\t\tnumCirclesToShow = Math.pow(2, circlePower);\n\t\t} else if (resetCountdown === 0) {\n\t\t\tcirclePower = 0;\n\t\t\tnumCirclesToShow = Math.pow(2, circlePower);\n\t\t\tresetCountdown = numLoopsAtMax;\n\t\t\tctx.clearRect(-radius, -radius, width, height);\n\t\t} else {\n\t\t\tresetCountdown -= 1;\n\t\t}\n\t\tconsole.log(`Showing ${numCirclesToShow} circles. Reset Countdown = ${resetCountdown}`);\n\t}\n});\n\n\n// add controls\nfunction updateConfig() {\n\tradius = +d3.select('#radius').node().value;\n\tplotAreaWidth = width - 2 * radius;\n\tplotAreaHeight = height - 2 * radius;\n  xScale.range([0, plotAreaWidth]);\n  yScale.range([0, plotAreaHeight]);\n\n\ttickAmount = +d3.select('#tickAmount').node().value;\n\tcolorInterpolator = d3[d3.select('#colorInterpolator').node().value];\n\trawColorScale.interpolator(colorInterpolator);\n\n\tctx.restore();\n\tctx.save();\n\tctx.translate(radius, radius);\n\tctx.clearRect(-radius, -radius, width, height);\n}\n\nd3.select('.controls').selectAll('input, select')\n\t.on('change', updateConfig);\n\n\n"]}

index.html

<!DOCTYPE html>
<title>Line Circle Illusion</title>
<style>
  body {
    padding: 30px;
    font-family: sans-serif;
  }

  .controls {
    margin-top: 30px;
  }

  label {
    display: inline-block;
    font-size: 12px;
    text-transform: uppercase;
    font-weight: 600;
    margin-right: 25px;
  }
  input, select {
    display: block;
    margin-top: 3px;
  }

  input {
    width: 50px;
  }
</style>
<body>
  <canvas></canvas>
  <div class="controls">
    <label>
      Radius
      <input type="number" id="radius" value="10" minValue="1" maxValue="100" step="1" />
    </label>
    <label>
      Tick Amount
      <input type="number" id="tickAmount" value="0.01" minValue="0.01" maxValue="0.2" step="0.01" />
    </label>
    <label>
      Color
      <select id="colorInterpolator">
        <option value="interpolateRainbow">Rainbow</option>
        <option value="interpolateMagma">Magma</option>
        <option value="interpolateInferno">Inferno</option>
        <option value="interpolateViridis">Viridis</option>
        <option value="interpolateWarm">Warm</option>
        <option value="interpolateCool">Cool</option>
      </select>
    </label>
  </div>
	<script src='https://d3js.org/d3.v4.min.js'></script>
	<script src='dist.js'></script>
</body>

preview.png

script.js

const tau = Math.PI * 2;

const width = 400;
const height = 400;
let radius = 10;
let plotAreaWidth = width - 2 * radius;
let plotAreaHeight = height - 2 * radius;

// corresponds to speed of circles. can be fun to play with.
let tickAmount = 0.01;

// we get 2^power number of circles drawn
const maxCirclePower = 9;
let circlePower = 0;
let numCirclesToShow = Math.pow(2, circlePower);

// after we have reached max power, how many loops
// before resetting to 1 circle?
const numLoopsAtMax = 4;
let resetCountdown = numLoopsAtMax;

// set the color scheme here:
let colorInterpolator = d3.interpolateRainbow;

// create the canvas
const screenScale = window.devicePixelRatio || 1;
const canvas = d3.select('canvas')
  .attr('width', width * screenScale)
  .attr('height', height * screenScale)
  .style('width', `${width}px`)
  .style('height', `${height}px`)
const ctx = canvas.node().getContext('2d');
ctx.scale(screenScale, screenScale);
ctx.save();
ctx.translate(radius, radius);

// position scales
const xScale = d3.scaleLinear().domain([0, 1]).range([0, plotAreaWidth]);
const yScale = d3.scaleLinear().domain([0, 1]).range([0, plotAreaHeight]);
const angleScale = d3.scaleLinear().domain([0, 1]).range([0, Math.PI]);
const positionScale = d3.scaleLinear().domain([0, Math.PI]).range([1, 0])

// colors-- we want to repeat every 3 trips while looping from one end
// to the other and back to the beginning.
const colorScaleMapper = d3.scaleLinear()
	.domain([0, 1, 1.5, 2, 3])
	.range([0, 0.6666666667, 1, 0.666666667, 0])

// t goes from 0 to 2
const rawColorScale = d3.scaleSequential(colorInterpolator);
function colorScale(t) {
	return rawColorScale(colorScaleMapper(t))
}


// create circles by adding in levels based on powers of 2
function createCircles() {
	let circles = [];
	for (let i = 0; i <= maxCirclePower; i++) {
		circles = circles.concat(createCirclePower(i));
	}

	return circles;
}

/*
  create circles for a given power of 2.
  e.g.:
	power=0  1,
	power=1  1/2,
	power=2  1/4 3/4
	power=3  1/8 3/8 5/8 7/8
	power=4  1/16 3/16 5/16 7/16 9/16 11/16
*/
function createCirclePower(power) {
	const denominator = Math.pow(2, power);
	const numCirclesToAdd = Math.pow(2, Math.max(0, power - 1))

	const circleRing = d3.range(numCirclesToAdd).map((i) => {
		const angle = angleScale(((2 * i) + 1) / denominator);
		return createCircle(angle);
	});

	return circleRing;
}

// create a single circle at a given angle
function createCircle(angle) {
	const baseRadius = 0.5;
	const tPosition = positionScale(angle);

	// use polar coordinates
	const sx = baseRadius * Math.cos(angle) + baseRadius;
	const sy = baseRadius * Math.sin(angle) + baseRadius;
	const tx = baseRadius * Math.cos(angle + Math.PI) + baseRadius;
	const ty = baseRadius * Math.sin(angle + Math.PI) + baseRadius;

	// linear interpolate with quadratic easing (easing should match update func)
	const t = d3.easeQuad(tPosition);
	const x = (1 - t) * sx + t * tx;
	const y = (1 - t) * sy + t * ty;

	return {
		tPosition,
		direction: 1,
		color: tPosition * 3,
		x,
		y,
		sx,
		sy,
		tx,
		ty,
	};
}

// draw circles on screen
function draw(circles) {
	ctx.save();

	let circle;
	for (let i = 0; i < circles.length && i < numCirclesToShow; ++i) {
		circle = circles[i];
		ctx.beginPath();
		ctx.arc(xScale(circle.x), yScale(circle.y), radius, 0, tau)
		ctx.fillStyle = colorScale(circle.color);
		ctx.fill()
		ctx.closePath();
	}

	ctx.restore();
}

// update circle positions
function update(circles) {
	let circle;
	for (let i = 0; i < circles.length; ++i) {
		circle = circles[i];

		// update position
		circle.tPosition = Math.max(0, Math.min(circle.tPosition + tickAmount * circle.direction, 1));
		if (circle.tPosition === 1 || circle.tPosition === 0) {
			circle.direction *= -1;
		}

		// important to use quadratic easing to get the circle illusion shape
		const t = d3.easeQuad(circle.tPosition);
		circle.x = (1 - t) * circle.sx + t * circle.tx;
		circle.y = (1 - t) * circle.sy + t * circle.ty;

		// update color
		circle.color = circle.color + tickAmount;

		// fix rounding error
		if (circle.color + 1e-6 > 3) {
			circle.color = 0;
		}
	}
}


// create the circles and draw them
const circles = createCircles();
draw(circles);

// begin a timer for doubling the number of circles at regular intervals
let timer = d3.timer((elapsed) => {
	update(circles);
	draw(circles);

	// if the first circle is back in start position, add a new ring
	if (circles[0].tPosition === 0) {
		if (circlePower < maxCirclePower) {
			circlePower += 1;
			numCirclesToShow = Math.pow(2, circlePower);
		} else if (resetCountdown === 0) {
			circlePower = 0;
			numCirclesToShow = Math.pow(2, circlePower);
			resetCountdown = numLoopsAtMax;
			ctx.clearRect(-radius, -radius, width, height);
		} else {
			resetCountdown -= 1;
		}
		console.log(`Showing ${numCirclesToShow} circles. Reset Countdown = ${resetCountdown}`);
	}
});


// add controls
function updateConfig() {
	radius = +d3.select('#radius').node().value;
	plotAreaWidth = width - 2 * radius;
	plotAreaHeight = height - 2 * radius;
  xScale.range([0, plotAreaWidth]);
  yScale.range([0, plotAreaHeight]);

	tickAmount = +d3.select('#tickAmount').node().value;
	colorInterpolator = d3[d3.select('#colorInterpolator').node().value];
	rawColorScale.interpolator(colorInterpolator);

	ctx.restore();
	ctx.save();
	ctx.translate(radius, radius);
	ctx.clearRect(-radius, -radius, width, height);
}

d3.select('.controls').selectAll('input, select')
	.on('change', updateConfig);

thumbnail.png