Welcome
This website provides access to data for the work of E. Goodman and CY Siu, who were supervised by R. S. Strichartz, in the 2016 Summer Program for Undergraduate Research (SPUR) Fractals Group.
The studied fractal is similar to the Sierpinski Carpet—which is shown at the top left of the page—although various identifications and other changes are made; more details will come soon. Note that this fractal is similar to that studied in the paper by Bello, Li, and Strichartz.
These pages are still under construction.
References & Acknowledgements
Other pages contain only pictures and data, so we collect here references we used in different parts of our research, along with other acknowledgements. References include, for fractals:
- Robert S. Strichartz, Differential equations on fractals: A tutorial, Princeton University Press, Princeton, New Jersey, 2006.
- Jason Bello, Yiran Li, and Robert S. Strichartz, Hodge-de Rham theory of k-forms on carpet type fractals, Excursions in Harmonic Analysis (Radu Balan, Matthew J. Begué, John J. Benedetto, Wojciech Czaja, and Kasso A. Okoudjou, eds.), vol. 3, Springer International Publishing, Switzerland, 2015, pp. 23–62.
For effective resistance of electrical networks:
- Peter G. Doyle and J. Laurie Snell, Random walks and electric networks, The Mathematical Association of America, Washington D.C., 1984.
- Wolfgang Woess, Random walks on infinite graphs and groups, Cambridge University Press, Cambridge, 2000.
This site contains many results of computations done using the Python Programming Language (http://www.python.org/). Particularly, several of the numerical compuations involved the use of the NumPy (http://www.numpy.org/) and SciPy (http://www.scipy.org/) packages. Plots were generated with the package matplotlib (http://matplotlib.org/).
E. Goodman was supported by the Haverford College Koshland Integrated Natural Sciences Center.
CY Siu was supported by the Professor Charles K. Kao Research Exchange Scholarship 2015/16.
Contact Information
R. S. Strichartz, Cornell University Mathematics Department, str@math.cornell.edu
E. Goodman, Haverford College, etgoodman@haverford.edu
CY Siu, The Chinese University of Hong Kong, alexcysiu@gmail.com