Bio

During Garrett’s high-school years, he conducted research in several areas of traditional science, such as behavioral ecology, physiological biophysics, and computational neuromorphology. In 2004, he worked as a research fellow at SUNY Stony Brook in the Department of Ecology and Evolution, where he used geometric morphometrics to study the differences in brain shape between two ecologically contrasting freshwater populations of threespine stickleback fish. In September of 2005, Garrett entered New York University’s (NYU) College of Arts and Science as a chemistry major and a pre-medical student. He found work with Professor Ray C. Dougherty (another NKS 2007 Summer School participant) in the NYU Linguistics Department where he began to study the geometrical evolution of the cochlea of various animal species and compare this evolution with that of the mollusc shell. Recent work with Dougherty includes various biolinguistic studies, which were presented at the Biolinguistic Investigations conference in the Dominican Republic. In his second year at NYU, Garrett switched his major to neural science, with a minor concentration in mathematics. Garrett now also works with John Rinzel of the NYU Center for Neural Science on matters of computational neuroscience. When taking a break from science and mathematics, Garrett performs and composes music. He has been playing the piano for fifteen years and the tuba for eight years. He currently performs in the NYU Wind Ensemble. His favorite composers are John Williams, Igor Stravinsky, and Gustav Holst (in that order).

Project: A Cellular Automaton Model of Dynamical Fitness Consequences of Different Reproductive Strategies

Biological organisms have evolved two principal mechanisms for effective propagation: asexual and sexual reproduction. A model is constructed in which a cellular automaton rule represents the species of a population, and initial conditions represent the genomes of individuals. One population of asexually reproducing cellular automata of a certain rule is subject to a certain “selective pressure”, while another population of cellular automata of the same rule is subject to the same selective pressure, but includes sexual reproducers. The fitness of individuals in successive generations as a function of time is examined in both the asexual and sexual cases for several elementary cellular automaton rules.

Project-Related Demonstrations

The Tree of Life

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 10818633

The 3-color outer totalistic rule 10818633 is of interest because early on in its evolution of a quite striking pattern bounded on both sides by repetitive structures, an unsightly triangle suddenly appears, ostensibly never to be seen again in the evolution of the cellular automaton. This reminds me of the saying, “a beautiful theory destroyed by an ugly fact.” Indeed, since the triangle occurs quite early on in the cellular automaton evolution, the base of the “theory” has crumbled. This is an often disappointing, yet necessary truth in science. Here is the code for 500 steps of evolution:

ArrayPlot[CellularAutomaton[{10818633,{3,{3,1,3}}},{{1},0},500],
ColorRules->{1->Red,2->Blue}]