Developmental variation in brain-wiring contributes to behavioural individuality1,2. However, how and when individualized wiring diagrams emerge and become stable during development remains largely unknown. Here, we explored axon targeting dynamics in individual brains using live-imaging of a developing Drosophila visual circuit and discovered that targeting choice is an algorithmic multi-step growth process with variable outcomes. Using optogenetics, we found that temporally restricted Notch lateral-inhibition defines a subset of neurons with a probabilistic potential to innervate distal targets. Next, axons from NotchOFF neurons amplify into long actin-rich multi-fibre structures necessary for distal growth. A subset of these NotchOFF neurons create distal targeting axons by stabilizing microtubule growth in one of their actin fibres. Amplified axons without tubulin-stabilized fibres retract, resulting in the stochastic selection of a different number of distal targeting axons in each brain. Pharmacological microtubule destabilization suffices to inhibit this targeting. We observed a similar axonal amplification-stabilization process in the developing chick spinal cord, suggesting a conserved mechanism. Finally, early microtubule patterns predict the adult brain- wiring of an individual in a target-independent manner prior to synapse formation3,4. Thus, we show that a temporal succession of genetically encoded stochastic processes explains the emergence of individual wiring variation.