a large number approximating a simple symmetry.
The symmetry of Pisano periods consists of prime factors: 2, 3, 5, 7, …n and their multiples. Between two perfect symmetries, consider the square numbers 5x5=25 and 6x6=36, consists a myriad of alternate factorizations, 26 through 35, such as 2x13 and 5x7. Each prime factor of a given modulus contributes to the numerical progression of a Pisano period, effecting its shape—considering a spatial representation of the numbers. Thus, a morphology exists between modulos and their constituent Pisano periods: from dipole to triangle, square, pentagon, and so forth with a myriad of asymmetrical prime factors inbetween. In another sense, there are infinite multiples of prime factors; in principle, the mind can grasp infinitely large numbers that comprise of simple factors.
My current aim is to develop an intuitive understanding of this morphology through time-based visualizations, while studying the analytical tools necessary to manipulate these relationships symbolically. Naturally, I will abstract these relationships into general principles, and apply them as navigational tools for further research: including the multimodal representation of numbers in space and time, to imprint complex, efficiently networked information on our thinking organs.