Random walk 10/28/08

For class today we attempted to use Mathematica to come up with a simple code to write a random path with the use of probabilities. This is the code Gary, Matt and I came up with:
(*This makes the first step of the random path.*)
randompath = {{0, 0}};
(*This defines the neighbors of the point{x,y}.*)
left[{x_, y_}] := [...]

Random walk1

In class we were introduced to the random walk concept. Elise came up with a concept that:
n= number  of steps
m= number of vertices
x= number of open vertices at each steps
Have been           Have not been at a place
P(x)= n/m           P(1-x) = 1-n/m
x >= 3   creates four mini squares in a pane
P(x=1) = (1- n/m)
P(x=2) = (1- n/m)^2
P(x=3) [...]

Prob. min memory path ending

In our class discussion we attempted to find the min memory path ending for the random walk graph. We decided it was 7 since if we start at a point there is only four possible moves left, right , up, dpwn(l,r,u, d). The branches of the four possible moves then create there own three possible moves since [...]

Random Walk

Two weeks ago we attempted to do random walk starting at zero. Prof. Davis created a Mathematica program to show a random walk graph. He kept changing the values to get the session time it took to walk. Starting it a zero there is only four possible moves left, right, up or down (l, r, [...]

Tower of Hanoi 4 peg

In class on Sept. 30, 2008, we had an interesting session. Elise and Adam lead the class with their recursive patterns for solving the 4 peg system.  The concept was that a 3 peg sytem can be used to give the answer for the minimal amount of moves needed to solve a 4 peg system. [...]

Tower of Hanoi

The edges of the graph are the legal moves of a single top disc. The graph is simple, connected and on a plane. For the Pascal triangle the odd numbers are the legal move and can be connected to form simple, connected triangle on a graph.

Tower of Hanoi

In playing the Tower of Hanoi for a 3 peg with n amount of disk. In order to get the least amount of moves, in class, we derived the formula
M(n) = 2*m(n-1) + 1
M(n)= m(n-1) + 1+ M(n-1)
M(n)= # of moves for n disk. This formula hold true for all n disks on a 3 [...]

Tower of Hanoi, Pascal triangle and sierpinski triangle

I realized that the Sierpinski graph is obtained from drawing a closed equilateral triangle. If we delete the middle triangle and do the same for the subtriangles we end up with the same graph has the tower of Hanoi. The pascal triange Graph if attach all the odd numbers forming triangles we have the [...]

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