My research interests are in fractals and chaos, and their applications and implications for art and culture. After completing the Ph.D., I worked closely with Dr. Benoit Mandelbrot (the “father” of fractals), and made major research contributions to condensed matter physics and to the techniques, images, and applications of fractal geometry.
I enjoy stimulating student and public interest in science, computers, and mathematics through fractals. I was one of the PI's on an NSF sponsored project to promote fractals and chaos as part of undergraduate mathematics education at Yale. I have been co-PI on 3 successive NSF sponsored Teacher Enhancement research grants. The most recent project was a NSF/FAU Math Science Partnership Institute to provide innovative graduate level education to middle school mathematics teachers in Broward County Florida.
My fundamental research includes low temperature macroscopic quantum phenomena in Josephson junction devices, 1/f noise, and the fractal characteristics of random media, growth processes, music and literature. Recent work is highly interdisciplinary, focusing on computational physics and complex dynamic systems via new applications of fractal concepts to diffusion limited aggregation, economic time series, correlations in DNA nucleotide sequences (including evolutionary trends), long range correlations and structure in natural languages (literature) and music, landscape generation and characterization, and image analysis (from art historical classification of early Chinese landscape paintings to detection of breast cancer from enhancement of x-ray mammograms).
I have long been interested in strengthening the connections between mathematics, science, art, and music through collaborations across traditional interdisciplinary boundaries.