Author(s)： Monique Chyba, Frederic Mercier, John Rader, Vanessa Douet, Eri Arikawa-Hirasawa, Youngsu Chow Kwon and Rich Kodama

J. Math-for-Ind. 3A (2011) 79-88.

• File： JMI2011A-8.pdf (5727KB)

Abstract
Within the last 20 years, new biological structures called fractones, named in honor ofthe late Dr. Benoit Mandelbrot due to their fractal-like appearance, have been discovered by cellbiologists. Their primary purposes are theorized to pertain to the major processes of the life cycleof cells, namely cell division, migration, and differentiation. Building on the back of the discretizeddiffusion equations, we built a mathematical model of how these fractones interact with the cellsand the associated growth factors produced in order to gain insight into the growth process as a whole. As it is shown in this paper, the complexity of this biological process opens the door to entirely new questions in the field of control theory.

Keyword(s).　 Morphogenesis, Fractones, Control Theory, Computational Modeling