Welcome to D.W. Jakel's homepage


Lyapunov exponents for the quadratic iterator

Acknowledgement: All diagrams in this page were produced in Java using F. A. Dushin's PlotTool classes

I am a graduate student in the Computer and Information Science program, Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY, 13244.

In the spring 1999 semester, I was the TA for two courses:

In the fall 1998 semester, I was the TA for two courses:

In the spring 1999 semester, I was the TA for two courses:

For biographical information, see my vita (a PostScript document)

Time-Space diagrams for cellular automata for the Fermi-Pasta-Ulam wave equation.
These diagrams were produced using algorithms by D. N. Ostrov and R. Rucker.

Ostrov and Rucker's "sushi".
The horozontal dimension is the cell space. The vertical dimension is time, increasing from top to bottom.
The initial configuration consists of two cycles of a sine curve.
 FPU.gifs/sine_1.gif


"Diamonds and nested squares"
The vertical dimension is the cell space. The horozontal dimension is time, increasing from left to right.
The initial configuration is shown as a line graph to the left of the main diagram, with the vertical dimension as the cell space, and the horozontal dimension as the state space.


"Nested diamonds and nested rectangles"
The vertical dimension is the cell space. The horozontal dimension is time, increasing from left to right.
The initial configuration is shown as a line graph to the left of the main diagram, with the vertical dimension as the cell space, and the horozontal dimension as the state space.

"Small sushi and large ornaments"
The vertical dimension is the cell space. The horozontal dimension is time, increasing from left to right.
The initial configuration is shown as a line graph to the left of the main diagram, with the vertical dimension as the cell space, and the horozontal dimension as the state space.

"Tangent wave"
The horozontal dimension is the cell space. The vertical dimension is time, increasing from top to bottom.
The initial configuration consists of one cycle of a tangent curve.


"Lakes and plowed fields"
The horozontal dimension is the cell space. Tthe vertical dimension is time, increasing from top to bottom.
Order begins to emerge from a random initial configuration.


The image below depicts part of the complex plane.
The horozontal position and vertical position of a point are the imaginary part and the real part, respectively, of the complex number represented by the point.
(This is the opposite of the usual convention.)
The portions of the real and imaginary axes which are outside the Mandelbrot set are shown in red.
The Mandelbrot set is shown in cyan.
All other points are shown in white, blue, or pink depending on the escape velocity.


A detail from the preceding image.



A detail from the detail.



A detail from the detail from the detail.



Comments? Please e-mail:

David W. Jakel (dwjakel@ecs.syr.edu)