Abstract
A Brownian motion process is introduced on iteratively reduced domain for evaluating capturing probability of not-yet-identified fractal attractor. Under the open set condition, the capturing probability is shown to be represented as a multi-scale image on which discrete feature points are well-defined. By combining a statistical separation condition, the feature points are shown to be clustered into subsets associated with reduced attractor. The discrepancy of attractor and associated mapping description due to clustering and location errors of feature points are estimated via structural and geometric analysis.
