These talks will be self-contained presentations of mathematical concepts
and theorems. They are intended to be accessible to all mathematics
students. Coffee, tea and drinks will be provided.
1 pm, Tuesday 20th March 2001
Science Lecture Theatre S14
Pascal's Triangles, Fractals and Cellular Automata
Dr Aidan Sudbury
Dept. of Mathematics & Statistics
Monash University
"Pascal's triangle" was originally constructed by the Chinese, though Blaise Pascal was the first person in the West to discover many of its patterns. The top of the triangle and it's sloping sides are all 1's; then, all the "combinations" (nCr) can be reached by adding elements of the rows above. Many interesting patterns have been found in this triangle.
The values of nCr that are odd can be seen to form a fractal pattern. A formula
for determining which values are odd can be derived by considering the growth of
a population of cellular automata, particles that occupy positions on a lattice
and interact with each other.