Fractal Renderer

Experience the beauty of fractals in your browser.

Try It!

What are Fractals?

Look above and see for yourself!

Fractals are infinitely complex patterns created by mathematical equations. One of their interesting aspects is that larger patterns often repeate themselves at smaller scales.

So I'm looking at math?

The results of using some math!

Here's how it works. First, for each pixel in the image, we generate a sequence of numbers. We generate this sequence by using a mathematical equation. Each fractal has its own unique equation.

Let's see how to generate a sequence of numbers for a pixel in the Mandelbrot Set. First we take the equation. For the Mandelbrot Set, this is:

next number in sequence = previous number squared + location of pixel as a number

(or at least, thats the simple way of writing it. Mathematicians write it like this: zn+1 = z2 + c)

Pretty simple, right? Let's try applying it. Suppose we had a pixel whose location corresponded to the number 1. Since we don't have a previous number, we set the "previous number" part of the equation to 0. So now we have:

next number in sequence = 02 + 1

Now we can just find the next number in the sequence. (Its 1). If we keep on applying this formula, we get the sequence:

1, 2, 5, 26…

The numbers will get bigger and bigger as we keep on running the equation. But so what? How does this help us get pretty pictures?

Here's how: We count how long it took for the numbers in the sequence to get larger than 2. So in this case, the result of doing that would be 2. Then we display the color that corresponds to the number. It's that simple.

But what about areas that are black? Are those special?

They ARE special! There are some numbers whose sequences NEVER get larger than 2. For example, the sequence for -1 is:

-1, 0, -1, 0…

Since this sequence repeates forever, it never gets larger than 2. These numbers are "inside the set" and we color them black.

If you'd like to know more about the Mandelbrot Set and other fractals, (and there's a lot more to learn!) check out the Wikipedia Article

What does Fractal Renderer do?

Lots of things!
  • It can render fractals in lots of pretty colors!
  • You can zoom in to 10,000,000,000,000,000 times magnification!
  • It allows you to view and explore a bunch of famous fractals such as the Mandelbrot Set and the Burning Ship Fractal!
  • You can also even enter a mathematical equation and create your own fractal!

So what are you waiting for?

Try it out!