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Using many features of Ian Wilson's Tidal Torque theory, a mathematical model of the sunspot cycle has been created that reproduces changing sunspot cycle lengths and has an 85% correlation with the sunspot numbers from 1749 to 2013. The model makes a reasonable representation of the sunspot cycle for the past 1000 yr, placing all the solar minimums in their right time periods. More importantly, I believe the model can be used to forecast future solar cycles quantitatively for 30 yr and directionally for 100 yr. The forecast is for a solar minimum and quiet Sun for the next 30 to 100 yr. The model is a slowly changing chaotic system with patterns that are never repeated in exactly the same way. Inferences as to the causes of the sunspot cycle patterns can be made by looking at the model's terms and relating them to aspects of the Tidal Torque theory and, possibly, Jovian magnetic field interactions.