In this paper, we focus on a challenging Online Task-Free Class Incremental Learning (OTFCIL) problem. Different from the existing methods that continuously learn the feature space from data streams, we propose a novel compute-and-align paradigm for the OTFCIL. It first computes an optimal geometry, i.e., the class prototype distribution, for classifying existing classes and updates it when new classes emerge, and then trains a DNN model by aligning its feature space to the optimal geometry. To this end, we develop a novel Dynamic Neural Collapse (DNC) algorithm to compute and update the optimal geometry. The DNC expands the geometry when new classes emerge without loss of the geometry optimality and guarantees the drift distance of old class prototypes with an explicit upper bound. Then, we propose a novel Dynamic feature space Self-Organization (DYSON) method containing three major components, including 1) a feature extractor, 2) a Dynamic Feature-Geometry Alignment (DFGA) module aligning the feature space to the optimal geometry computed by DNC and 3) a training-free class-incremental classifier derived from the DNC geometry. Experimental comparison results on four benchmark datasets, including CIFAR10, CIFAR100, CUB200, and CoRe50, demonstrate the efficiency and superiority of the DYSON method. The source code is provided in the supplementary material.