Activity dependent synaptic plasticity is widely believed to play the major role in learning and memory. Moreover, the robustness of formed memories is dependent on the stability of synapses. However, recent studies have shown that synapses undergo a significant volatility which are activity independent [1]. This stochastic turnover therefore can put a great challenge on encoding and preserving information in synaptic connectivity [2]. In this study, using in vivo STED nanoscopy, morphological features of excitatory spines in mouse cortical circuits including head size, neck length, and neck width were measured in the short (hour) and long (day) intervals for up to 30 days monitoring their changes in time. We model two scenarios where the change of spine morphological features could be activity dependent (based on the timing of learning events following a Poisson distribution) or completely spontaneous (stochastic dynamics of actin filaments). Comparing cross correlation functions of spines’ features we could distinguish distinct roles of activity (in)dependent plasticity in governing synaptic turnover over short and long-time intervals. Our results show that quenched disorder – the heterogeneity in the stable component of synaptic measures – is necessary to capture non-vanishing part of cross correlation functions that our data suggests.