Acute myeloid leukaemia (AML) is a haematologic malignancy with high relapse rates in both adults and children. Leukaemic stem cells (LSCs) are central to leukaemopoiesis, treatment response and relapse and frequently associated with measurable residual disease (MRD). However, the dynamics of LSCs within the AML microenvironment is not fully understood. This study utilized three-dimensional cellular automata (CA) modelling to simulate LSC behaviour and treatment response under induction chemotherapy. Our study revealed: (i) a correlation between LSC persistence post-induction chemotherapy and risk of AML relapse; (ii) MRD negativity based on LSC count may not reliably predict outcomes, supporting clinical evidence that patients with MRD-negative status can still be at risk of relapse; (iii) prolonged persistence of LSCs post-chemotherapy without disruption of normal haematopoiesis, aligning with clinical observations of dormant AML clones; (iv) early LSC dynamics post-induction chemotherapy, characterized by stochastic behaviours and movement velocities, are insufficient predictors of long-term prognosis; and (v) a distinct spatiotemporal organization of LSCs in later phases post-induction chemotherapy is correlated with long-term outcomes. Our modelling results provide a theoretical and clinical framework for AML research, and future clinical data validation could refine the utility of CA modelling for oncological studies.