Close, dense, compact, thick are comparable when they mean having constituent parts (as filaments, particles, cells, or atoms) that are massed tightly together.
Close may apply to the texture or weave of something. More often, however, the term applies to something that is made up of a number of single things pressed or seemingly pressed together. Especially as applied to literary expression, close implies a compression of what is to be said into the fewest and most telling words possible.
Dense applies to something in which the arrangement of parts or units is exceedingly close. The term commonly implies impenetrability and in extended use may lose the basic notion of close packing of parts.
Compact suggests close and firm union or consolidation of parts, especially within a small compass; it often also implies neat or effective arrangement.
Thick (see also STOCKY) usually applies to something which is condensed or is made up of abundant and concentrated parts.