I was able to solve the heat equation, but am unsure of how to graph the partial sums of the solution.
a.) Solve the heat equation subject to
u(0, t) = 0, u(100, t)=0, t>0
u(x, 0) = 0.8x, 0 ≤ x ≤ 50
u(x, 0)=0.8(100-x), 50 < x ≤ 100
b.) Use the 3D plot application to graph the partial sums consisting of the first five nonzero terms of the solution in art a for 0 ≤ x ≤ 100, 0 ≤ t ≤ 200. Assume that k=1.6352. Experiment with various three-dimensional viewing perspectives of the surface.
I was able to get part a, but am unsure of how to code part b in Mathematica.
Ok so I made a simple program using turtle in python ,basicly its a turtle enclosed in a double loop;it moves foward a bit and then it moves right x where x is equal to 1,1,2,1,2,3,1,2,3,4,,etc for those who understand pseudocode its the following
for i from 1,2500:
for x from 1,i:
turtle.fw(1) //Or something smaller to zoom out
now it makes the following
pretty random just a lot of spirals, but if I zoom out by a factor of a hundred…
it makes a beautiful pattern, how does this patter emerge out of a random set of spirals? Also If you change
turtle.right(x*80) it makes this:
still preaty random.. however if you zoom out by 10 this patern emerges:
y=71 to any number you wish, I have Checked that any repetitive 8’s make an incredible patern (8,88,888,etc) and that repetitive nines always make a straight line. If anyone has any idea why this patterns emerge or have any idea even what subject or sector of math invesigates 2d patterns from simple instructions It would be of great help!