Random Walk to Fit Trigonometric Functions, and Its Implications

Years ago, initially we demonstrated that the global temperature-time profile could be perfectly fitted using the random walk in either 1/-1 or decimal forms generated by the Monte Carlo simulation. Later on, we found that the random walk simulation was applicable to the precipitation-time, stock index-time and commodity price-time profiles. Strictly speaking, these curves are not time function, but natural phenomena recorded according to a certain equal interval along the time course. In this study, we extended our simulation to trigonometric functions, which do not involve the time. The results demonstrate that the trigonometric functions, sin, cos and tan can be fitted by the random walk in both 1/-1 and decimal forms. It implies that the defined relationship between independent and dependent at macro scale can be simulated by random events at micro scale. Although we are not aware whether there is a single path or trajectory that a particle can take in quantum mechanics is equivalent to random values generated by the Monte Carlo simulation, our study suggests the beginning to link the behavior of particles in micro world with the behavior of maters in macro world.