  Consider a network $D$ of pipes which have to be cleaned using some cleaning
agents, called brushes, assigned to some vertices. The minimum number of
brushes required for cleaning the network $D$ is called its brush number. The
tattooing of a simple connected directed graph $D$ is a particular type of the
cleaning in which an arc are coloured by the colour of the colour-brush
transiting it and the tattoo number of $D$ is a corresponding derivative of
brush numbers in it. Tattooing along an out-arc of a vertex $v$ may proceed if
a minimum set of colour-brushes is allocated (primary colours) or combined with
those which have arrived (including colour blends) together with mutation of
permissible new colour blends, has cardinality greater than or equal to
$d^+_G(v)$.
