The dynamic shape of coarse particles was determined by catastrophic tumbling studies performed in a rotating cylinder. Here, the dynamic shape was defined as the deviation from ideally regular and predictable tumbling behaviour. The data suggested that even with a comprehensive description of a static particle its transport properties cannot be accurately predicted. The fractal dimension in data space of the time series of events presents a method that can identify limits of predictability, and thus show regions that should be avoided to minimise the emergence of chaotic behaviour.