I created a presentation called: "Math is fun: Chaos Game".
 I want to show you an interesting method of generating fractals. (albo method to generate fractals, co wolisz)
 // on te slide we see Julia set
 Fractals in matematics are detailed, recursive and infinitely self-similar mathematical sets.
 I know it's a hard to understand that definition but
 Fractals don't have a strict definition because there is a huge variety of examples and there doesn't exist a universal definition
 for every fractal.
 I can show you some basic fractals, for examples:
 polish fractal: Sierpinski carpet
 it's a good example to understand how to create some fractals because not every fractal has a recursive
 funtion to generate it.

The construction of the Sierpinski carpet begins with a square.
The square is cut into 9  subsquares
and the central subsquare is removed.
The same procedure is then applied recursively to the other 8 subsquares and reapeted.


Chaos game is a simpe method of generating some fractals.
Firstly we must created 3 or more points. and we have to number them.
Secondaly we must create a start point. Now we can play.
We can use a dice to generate some random numbers.
But we dont have any xD because we are a poor students xD
Ok we must generate some random numbers like 1 2 3...
and draw new points. but how to draw new points?
we must get halfway between your last used point and your random number.

in this circle we never create new point. i dont have proof but belive me xD

create more.. and more and more..

i know its boring. but what happen when we created 1000 points? or more

we have a fractal "Sierpinski triangel" its a very interesting fractal because its  show 1.5 dimension but i can't explaint it.
and i don understand 1.5 dimension. but it is interesting in my opinion xD :( pepe_Cry

but what if we used more start points? like 4?
with ours old rules (half distance and random point) we can't created a interesting fractal.
But we can add more rules!

// tu musze coś napisać ale jeszcze nie wiem co

the last two(or more) corners can’t be chosen two times
We can invent a lot of rules :D

ok now i have some examples for fractals generated by chaos game with difrent rules
you can read it if you want xD

ok. last is my special example.
when we take six points and these are angels of ours triangels and we start play chaos game we get this fractal