It is known for a large number of transcendental entire functions with bounded singular set that every escaping point can eventually be connected to infinity by a curve of escaping points, now often called (Devaney) hairs. When this is the case, we say that the function is criniferous. Although not all functions with bounded singular set are criniferous, those with finite order of growth are, and, in some special cases, their Julia set is a collection of hairs forming a topological object known as Cantor bouquet. In this talk, we describe a new class of criniferous functions and explore their relation to Cantor bouquets. This is joint work with L. Rempe.

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