WEEK 1 (FRACTALS) 1-1) Play the following "line chaos game": You
need a coin , paper and pencil. Draw a segment across the page;
we will call its length "1". The left end is called H (for
Heads) and the right is called T (for Tails). Rules: Pick any
point in the segment (called Xo, the "seed"). Flip the coin. If
it turns up Heads then move the point toward the H end so that
its distance to H is 1/3 of the previous distance. Conversely,
if it is Tails then move the point toward the T end so that its
distance to T is 1/3 of the previous distance. Repeat... As an
exercise to practice the game, do the following sequence: Start
at the mid-point (Xo=1/2) and sketch the orbit for this
succesion of coin flips: H,H,T. You should get something like
this: Your job is to find out what object would emerge if you
would play this game for thousands of flips (that is, regardless
of the seed you start with, as long as you erase the first few
points, and the particular successions that might occur, is
there a PATTERN that emer