We construct a mathematical model of interface fluctuations in Czochralski crystal growth based on the thermal balance across the growing interface. The model describes time‐dependent growth rate in relation to fluctuations in crystal pull rate and melt flow viewed as external perturbations. Complexities in the flow of a silicon melt are characterized in terms of time series forecast about melt thermal fluctuations actually observed beneath a growing crystal. The melt exhibits self‐affine random motion with spatial and temporal structure specific to crucible rotation rate. The influence of the complex flow to crystal growth is discussed on the basis of the model proposed. ©1995 American Institute of Physics.