We describe an algorithm for constructing fractal Brownian motion clouds, characterised by three parameters: the fractal dimension, D (which determines the power spectrum of fluctuations), the density scaling parameter, S (which determines the density contrast between large and small structures), and the dynamic range, R (which determines the range of scales over which structure is resolved – due to either observational or numerical limitations). R is always known ab initio for any data set. We show that the other two parameters (D and S) can be estimated very accurately using a well-trained Convolutional Neural Network (CNN). In contrast, Delta Variance can only estimate D, and does so more slowly (in terms of computing overhead) and less accurately than the CNN. We conclude with a discussion of the limitations of this technique.