Growth cones sense cues by filopodial contact, but how their motility is altered by contact remains unclear. Although contact could alter motile dynamics in complex ways, our analysis shows that stable contact with Schwann cells induces motility changes that are remarkably discrete and invariant. Filopodial contact invariably induces local veil extension. Even when contacts are brief, veils always extend before the filopodia retract. Contact at filopodial tips suffices for induction. Moreover, veils extend significantly sooner than on filopodia contacting laminin, which often detach without extending veils. The overall behavioral responses of the growth cone, such as increased area and turning, result from integrating multiple discrete responses. Cycles of veil induction enlarge the growth cone and often lead it onto the cell. Invariant veil induction is abolished by blocking N-cadherin signaling. We propose an axonal guidance model in which different guidance cues act by inducing different but discrete and invariant responses.