Randomize setInterval ( How to rewrite same random after random interval)

Here's a reusable version that can be cleared. Open-sourced as an NPM package with IntelliSense enabled.

Utility Function

const setRandomInterval = (intervalFunction, minDelay, maxDelay) => {
  let timeout;

  const runInterval = () => {
    const timeoutFunction = () => {
      intervalFunction();
      runInterval();
    };

    const delay = Math.floor(Math.random() * (maxDelay - minDelay + 1)) + minDelay;

    timeout = setTimeout(timeoutFunction, delay);
  };

  runInterval();

  return {
    clear() { clearTimeout(timeout) },
  };
};

Usage

const interval = setRandomInterval(() => console.log('Hello World!'), 1000, 5000);

// // Clear when needed.
// interval.clear();

Something like this should work - use setTimeout() instead so you can set a new random value each time:

function doSomething() {
    alert("doing something");
}

function init() {
    var myFunction = function() {
        doSomething();
        var rand = Math.round(Math.random() * (3000 - 500)) + 500; // generate new time (between 3sec and 500"s)
        setTimeout(myFunction, rand);
    }
    myFunction();
}

$(function() {
    init();
});

Working jsFiddle here.

Here is a really clean and clear way to do it:

http://jsfiddle.net/Akkuma/9GyyA/

function doSomething() {}

(function loop() {
    var rand = Math.round(Math.random() * (3000 - 500)) + 500;
    setTimeout(function() {
            doSomething();
            loop();  
    }, rand);
}());

EDIT:

Explanation: loop only exists within the immediately invoked function context, so it can recursively call itself.

Just setup interval each time you rand (and clear it first)

function doSomething(){
     // ... do something.....
}

var i;
var rand = 300;

function randomize() {
    doSomething();
    rand = Math.round(Math.random()*(3000-500))+500; 
    clearInterval(i);
    i = setInterval('randomize();', rand);
}

i = setInterval('randomize();', rand);

or try using setTimeout (and setting again after randing)