Piercing the Deepest Mathematical Mystery

Using iterated self-convolutions of truncated strings, we build a system of dynamical systems, each with a different but very simple seed: a string consisting of n+1 digits, all zeros except a one at each end. The n-th system consists of strings with up to 2n digits, and after n iterations, the iterated string has the same first n-3 digits as the number e. By analyzing the non-chaotic behavior of each dynamical system during the first n iterations and letting n tend to infinity, we find spectacular patterns regarding the number of ones, leading to deep results regarding the digits of e. Computations used to identify the patterns involve numbers larger than 2^n + 1 at power 2^n, yielding about n correct digits of e, with n a large integer.