It is shown that the time series of sunspot counts may be represented as the sum of a regular cyclical process and a random Hurst process. In the 2375-month study period 1/1818-11/2015, the optimal cyclical components of mean monthly sunspot counts consist of a short wave function with a period of 131 months and a long wave function in which the amplitude of the short wave undergoes a 100-year cycle. The residuals of this model, though random, exhibit properties of the Hurst phenomenon in which dependence, memory, and persistence generate apparent patterns out of randomness. The findings imply that not all patterns in the empirical record of sunspot counts contain useful information because some patterns represent random behavior.