Gene expression is constantly regulated by gene regulatory networks that consist of multiple regulatory components to mediate cellular functions. An ideal tool for analyzing gene regulation processes would provide simultaneous measurements of the dynamics of many components in the gene regulatory network, but existing methodologies fall short of simultaneously tracking the dynamics of components over long periods of time. Here, we present CytoTape-a genetically encoded, modular, and scalable analog recorder for continuous, multiplexed recording of gene regulation dynamics over multiple days and weeks at single-cell resolution. CytoTape consists of a flexible, thread-like, elongating intracellular protein self-assembly engineered via AI-guided rational design. Gene regulation dynamics, together with timestamps for reconstruction of the continuous time axis, are directly encoded via distinct molecular tags distributed along single CytoTape assemblies in live cells, to be readout at scale after fixation via standard immunofluorescence imaging. CytoTape recorders are modularly designed to record gene expression driven by a variety of activity-dependent promoters. We demonstrated the utility of CytoTape in mammalian embryonic kidney cells, cancer cells, glial cells, and neurons, achieving simultaneous recording of five cell plasticity-associated transcription factor activities and immediate early gene expression levels, namely CREB, c-, , , and activities, within single cells in a spatiotemporally scalable manner. CytoTape revealed complex waveforms and nonlinear temporal couplings among these cellular activities, enabling investigations of how gene regulation histories and intrinsic signaling states shape transcriptional logics. We envision CytoTape to have broad applications in both basic and disease-related cell biology research.