Convert a number between 1 and 16777215 to a colour value

Question

I'm trying to convert a number between 1 and 16,777,215 to any colour format (RGB/HSL/HEX) that increments through the colour spectrum using Javascript/jQuery.

The number 16,777,215 is the total possible combinations of RGB(255,255,255) which is 32 bit colour.

I initially thought converting the value to a hex value using toString(16) would increment through the spectrum, however as the number increases it seems to work through different lightness values instead and flashes. An example of this unwanted behaviour is here http://jsfiddle.net/2z82auka/

var colour = 16777215;
window.setInterval(function(){
    colour -= 1000;
    $('body').css({background:'#' + colour.toString(16)});
}, 50);

How can I convert a value between 1 and 16777215 to a colour on the colour spectrum shown below?

Answer 1

The code below will do exactly what you want - it'll give you vibrant colors of the color spectrum exactly as the image below, and to prove it, the demo will print out the integer values beside the color. The result will look like this. Please use the rainbow function in your setInterval code.

var colours = 16777215;

function rainbow(numOfSteps, step) {
	var r, g, b;
	var h = 1 - (step / numOfSteps);
	var i = ~~(h * 6);
	var f = h * 6 - i;
	var q = 1 - f;
	switch(i % 6){
		case 0: r = 1, g = f, b = 0; break;
		case 1: r = q, g = 1, b = 0; break;
		case 2: r = 0, g = 1, b = f; break;
		case 3: r = 0, g = q, b = 1; break;
		case 4: r = f, g = 0, b = 1; break;
		case 5: r = 1, g = 0, b = q; break;
	}
	var c = "#" + ("00" + (~ ~(r * 235)).toString(16)).slice(-2) + ("00" + (~ ~(g * 235)).toString(16)).slice(-2) + ("00" + (~ ~(b * 235)).toString(16)).slice(-2);
	return (c);
}

function render(i) {
	var item = "<li style='background-color:" + rainbow(colours, i) + "'>" + i + "</li>";
	$("ul").append(item);
}

function repeat(fn, times) {
	for (var i = 0; i < times; i+=10000) fn(i);
}

repeat(render, colours);

li {
  font-size:8px;
  height:10px;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<ul></ul>

(I can't take credit for this code, but I can take credit for not giving up and settling for jerky color changes. Ref: https://gist.github.com/ruiwen/6163115)

Answer 2

Convert to range the initial value from 1 > 16777216 from 0 > 360

Technique here: Convert a number range to another range, maintaining ratio

Then use the HSL colour model, and increment from H0 S100 L100 > H360 S100 L100