A model of haematopoiesis that links self-organisation with symmetric and asymmetric cell division is presented in this paper. It is assumed that all cell divisions are completely random events, and that the daughter cells resulting from symmetric and asymmetric stem cell divisions are, in general, phenotypically identical, and still, the haematopoietic system has the flexibility to self-renew, produce mature cells by differentiation, and regenerate undifferentiated and differentiated cells when necessary, due to self-organisation. As far as we know, no previous model implements symmetric and asymmetric division as the result of self-organisation. The model presented in this paper is inspired by experiments on the Drosophila germline stem cell, which imply that under normal conditions, the stem cells typically divide asymmetrically, whereas during regeneration, the rate of symmetric division increases. Moreover, the model can reproduce several of the results from experiments on female Safari cats. In particular, the model can explain why significant fluctuation in the phenotypes of haematopoietic cells was observed in some cats, when the haematopoietic system had reached normal population level after regeneration. To our knowledge, no previous model of haematopoiesis in Safari cats has captured this phenomenon.