There is increasing evidence of fibril character in astrophysical magnetic fields. The solar photosphere is an obvious example. We suggest that the hierarchy of magnetic structures observed in the photosphere may be synthesized through the coalescence of the thin (Rroughly-equal2--3 x 10/sup 2/ km), intense (Broughly-equal1--2 x 10/sup 3/ gauss) magnetic fibrils seen to be threading the solar surface. Indeed, the distribution of magnetic flux tube sizes in a large-scale fibril magnetic field is likely to result from the interplay between flux tube coalescence and fragmentation.