We studied numerically the details of In compositional fluctuations and a spontaneous formation of a dot-like structure of InGaN alloy semiconductor due to phase separation by using the cell dynamical system (CDS) approach focusing on the details of the stage of time-evolution of phase separation. The numerical results in this work resemble the experimental results on inhomogeneouos alloying of InGaN reported so far and in addition predict the diffusion which previous experiments could not determine quantitatively. The In-rich regions with a dot-like structure appearing in InGaN-based multi-quantum-well (MQW) laser diodes (LDs) with their emission wavelength below 450nm are composed of InGaN showing small spatial fluctuations of In composition formed at an early stage of phase separation. The large blueshift of the static electroluminescence (EL) peak observed in blue and green InGaN-based single-quantum-well (SQW) light-emitting diodes (LEDs) above 450nm also relates to the large spatial fluctuations of In composition grown at an early stage of phase separation. For the higher In composition corresponding to the emission wavelength longer than 450 nm, the time-evolution of phase separation proceeds rapidly, indicating the large In compositional fluctuation and thus the large blueshift. In order to obtain a spatially uniform In composition, we should realize a uniform distribution of In composition during the growth of InGaN layer before phase separation proceeds.