Egolf, DA; Greenside, HS, *Stochastic to deterministic crossover of fractal dimensions for a Langevin equation*,
Physical Review E Statistical, Nonlinear, and Soft Matter Physics, vol. 47 no. 5
(1993),
pp. 3753-3756 [doi] .
**Abstract:**

*Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short-time scales to finite values of deterministic chaos at longer-time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos. © 1993 The American Physical Society.*