Alan Kaminsky Department of Computer Science Rochester Institute of Technology 4571 + 2426 = 6997
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Prof. Alan Kaminsky
Rochester Institute of Technology -- Department of Computer Science

Here are some interesting images I've produced. Click on an image to see a larger version.

MRI Spin Relaxometry
Wolfram's Rule 30 Cellular Automaton
Wolfram's Continuous Cellular Automaton
Cube Roots of 1
Mandelbrot Set
Prime Number Function


A depiction of the results of a spin relaxometry analysis of a magnetic resonance image (MRI) of a slice through someone's brain. The three colors highlight areas of the brain where the atomic spins relax at certain rates. For further information:


The evolution of Wolfram's Rule 30 cellular automaton. For further information:

The evolution of Wolfram's continuous cellular automaton. Each cell's value is a real number in the range 0.0 to 1.0. Each cell is updated by averaging the three cells in the neighborhood, applying a linear transformation, and truncating the integer part of the result. For further information:

The basins of convergence for the three complex cube roots of 1 (1+0i, −0.5+0.87i, and −0.5−0.87i). Each pixel's color represents the cube root of 1 to which a Newton iteration converges starting from the pixel's location. The basins' shapes are highly complex and, indeed, fractal. For further information:
  • William H. Press et al., Numerical Recipes in C, Second Edition (Cambridge University Press, 1992), pages 367-368.
  • Numerical Recipes Online. http://www.nr.com
  • Alan Kaminsky. M2MI Library, package edu.rit.parallel.fractal. (Javadoc)

The ever-popular Mandelbrot Set. For further information:
  • Benoit Mandelbrot, The Fractal Geometry of Nature (Henry Holt & Co., Inc., 1984).
  • Alan Kaminsky. Parallel Java Library, packages edu.rit.clu.fractal, edu.rit.smp.fractal. (Javadoc)

A graph of the prime number function π(x) = the number of primes <= x for x from 0 to 500. As x increases, π(x) jumps up by 1 whenever x is prime. The Prime Number Theorem says that for large x, π(x) is approximately equal to x / ln x.

Alan Kaminsky Department of Computer Science Rochester Institute of Technology 4571 + 2426 = 6997
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Copyright © 2005 by Alan Kaminsky. All rights reserved. Last updated 10-May-2006. Send comments to ark­@­cs.rit.edu.