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### Messages - Andi

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##### Presentations and discussions / Re: Julia Set
« on: April 05, 2017, 12:56:26 AM »
Julia Sets:
zn+1 = c sin(zn)   zn+1 = c exp(zn)
zn+1 = c i cos(zn)   zn+1 = c zn (1 - zn)

A property of the the Julia Set is that if the domain of c is real numbers the the Julia Set it mirrored about the Real axis. If  c is a complex number with an imaginary component then then the symmetry is rotational at 180 degrees.

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##### Presentations and discussions / Brownian Motion
« on: April 05, 2017, 12:46:37 AM »
Properties of Brownian Motion

Brownian Motion is defined to be the observable random motion of particles in fluids. The motion is described analytically using the Wiener Process.

There are 4 properties describing this motion:

1. B(0) = 0
2. For all time intervals  t ≥ 0 the increments B(t) are independent random variables.
3.  for all t ≥ 0 and h > 0, the increments B(t + h) − B(t) are normally
distributed with expectation zero and variance h. (meaning there is no bias towards a certain direction for any variance h)
4. The function described by the Brownian Motion is almost always continuous.

References:

http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/McKnight.pdf

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