Iterative Sierpinksi Fractal (drawn on HTML5 Canvas)

So maybe you’ve seen this very famous fractal called the Sierpinksi Fractal.

A few days ago I heard that you could create this fractal pattern by simply plotting out of a random sequence of mid points of an ever growing set of these mid points. So curiosity added with my apetite for playing with the HTML5 Canvas object and you have me playing on a saturday afternoon and then blogging about it.

Drawing this thing

Usually you’d think of drawing the Sierpinski Triangle the Recursive way, specially if you’re a CS student. The algorithm would be basically… For each triangle you create 3 triangles, one on top, one on the left, and one on the right (in the order that you want), repeat and rinse for each new triangle (until you decide to stop… you can use for example the height of the next triangle to stop, if too small stop)

But then I heard on some online video lecture about fractals that you could obtain the same results in an iterative fashion, no recursion whatsoever, just generate point after point randomly following one basic rule.

Choose 3 points in a plane, then choose 2 random points of the 3 and draw the middle point of these 2. Do the same for the new set of points. If the 3 initial points represent the vertices of a triangle you have yourself a Sierpinski fractal triangle. If you don’t choose an initial triangle, you’ll also get Sierpinski but it looks as if you were looking at the triangle from a random angle.

I must say I was pretty amazed when I saw it working… TADA!!!!


Try it on your browser
(Tested and works under Firefox 3.5, Chromium 4.0.2, and Safari)

That’s how it looks when you draw 800k random mid points.

PS: It runs faster in Chrome, props to Chrome developers.

HTML 5 is out and about

I believe that the <canvas>, <audio>and <video> tags will make the web a pretty exciting place. A lot of Flash components will be rewritten or converted into Javascript+HTML5 Object components making available more reusable elements for a graphical and interactive web, all being open sourced (javascript) and with no extra plugins needed.

Some places where we can already see (or will) the use of HTML 5 tags and javascript on those elements are:

  • GMail Mobile for iPhone and Android
  • Yahoo! Pipes
  • Bespin, a code editor created by Mozilla lab, they basically rewrote the text editing component using the canvas tag so that its a high performance text editing component, with a nice look, selection highlighting, new scrollbars, command support, it can be extended with your own commands (reminds me of emacs)
  • Google Waves
  • Some blogs that are already using the <article>, <nav>, <footer> and other new HTML 5 tags
  • YouTube is getting ready for the video tag