Monday, 6 December 2010

More on maths...

People won't believe where you can find maths. Like this:

"It's a fern leaf" you think.

Yes it is, but no, it is not. It's just the result of a recursive formula.

Look at the next one:

Every leaf of the fern is composed from smaller leafs that are the same, but rotated, shrinked and placed sequentially on the stem.

See where this is going?

The whole leaf is composed from smaller leafs, which are, in their turn, composed of even smaller leafs, which are, in their turn, composed of even ....

--> The previous sentence is the iteration process. How many times you want to compose something from smaller parts that look the same, but are rotated and translated, is called the iteration depth.

Computers are very happy to do the same thinover and over. They are our top iterators. They like it, because the need the instructions just once, and then they will repeat it to infinity. Or breakdown, if you're using XP.

So, recursive use of the same formula will lead us to some amazing effects:

A broccoli?
A recursive computer drawing. A fractal.

Look how a snowflake (Koch's snowflake) is formed by
  • dividing every side of a triangle in three parts,
  • Removing the middle part,
  • replacing the empty line with two triangulated parts,
  • repeating this over and over, on any scale.

Gotta close with some really interesting fractal art impression...

 There's more on fractals and recursion, So if you like it, let me know.

Courtesy to Wikipedia for most of the pictures.


  1. oh i love fractal geometry, it can be applied to all things in reality. every last experience in life is apart of a fractal

  2. Very nice fractal geometry trics :p ! Now I can see how maths are usefull :)

  3. Very interesting! More, please!

    Yes, every last experience in life is part of a fractal.

  4. see and when i finished up my last math class in college i said IM NEVER DOING THIS SHIT AGAIN. what i liar i am eh

  5. I can't wait to learn about this stuff in college.

  6. fractals have always been a mystery for me, now i finally find out what they are, thanks

  7. Math is omnipresent in our lifes!

  8. Wow... that's pretty mind-blowing.

  9. Love the way the snowflake was created like that! Nice explanation on the leaves to cause I remember staring at them seeing a bunch of others leaves connecting with each other.

  10. wow i fell like i see the world and all with the blood of art

  11. fractals are very intriguing, i have a folder of 'em that i use as backgrounds.. that snowflake .gif is awesome btw

  12. I wish I was more proficient at math, the language of god and all that

  13. Wow, that is so freaking cool. Damn it, math, why are you everywhere?!

  14. My mind: she has been blown. Following for sure.

  15. Pretty neat! Math is one amazing thing