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Studies on colour quantisation have indicated that its applications range from the relaxation of displaying hardware constraints in early years to a modern usage of facilitating content-based image retrieval tasks. Among many alternatives, approaches based on neural network models are generally accepted to be able to produce quality results in colour quantisation. However, these approaches using n quantised neurons require O(n) for a full search strategy, which is inefficient when n becomes large. In view of this, we propose to incorporate a growing quadtree structure into a self-organising map (GQSOM) which reaches a search time O(logn). Specifically, the strategy of inheriting from parent neurons hierarchically facilitates a much more efficient and flexible learning process. Both theoretical and empirical studies have shown that our approach is adaptive in determining an appropriate number of quantised colours, and the performance is significantly improved without compromise of the quantisation quality.