Brownian tree in an electrodeposition cell, and are the direct result of diffusion-limited aggregation. Brownian tree A Brownian tree, whose name is derived from Robert Brown via Brownian motion, is a form of computer art that was briefly popular in the 1990s, when home computers started to have sufficient power to simulate Brownian motion. Brownian trees are mathematical models of dendritic structures associated with the physical process known as diffusion-limited aggregation. A Brownian tree is built with these steps: first, a "seed" is placed somewhere on the screen. Then, a particle is placed in a random position of the screen, and moved
Geometric Brownian motion above: formula_27. import numpy as np import pandas as pd import matplotlib.pyplot as plt mu=1 n=50 dt=0.1 x0=100 x=pd.DataFrame() np.random.seed(1) for sigma in np.arange(0.8,2,0.2): x.columns=np.arange(0.8,2,0.2) plt.plot(x) plt.legend(x.columns) plt.xlabel('t') plt.ylabel('X') plt.title('Realizations of Geometric Brownian Motion with different variances\n mu=1') plt.show() GBM can be extended to the case where there are multiple correlated price paths. Each price path follows the underlying process where the Wiener processes are correlated such that formula_31 where formula_32. For the multivariate case, this implies that Geometric Brownian motion is used to model stock prices in the Black–Scholes model and is the most widely used model of stock