$\bullet$ $D_a$ determines how fast a diffuses.
$\bullet$ $\bigtriangledown^2_a$ determines the direction in which a diffuses.
$\bullet$ if a has low concentration at some cell then $\bigtriangledown^2_a$ will be positive and a will diffuse toward this cell.
$\bullet$ if a has high concentration at some cell then $\bigtriangledown^2_a$ will be negative and a will diffuse away from this cell.

Key point: a small amount of variation in the initial concentrations gives an initially unstable system which may then be driven to a stable state in which the chemical concentrations vary across the surface, producing a pattern.