"never-ending pattern," 1975, from French fractal, ultimately from Latin fractus "interrupted, irregular," literally "broken," past participle of frangere "to break" (from PIE root *bhreg- "to break"). Coined by French mathematician Benoit Mandelbrot (1924-2010) in "Les Objets Fractals."
Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that ... classical geometry ... is hardly of any help in describing their form. ... I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals — or fractal sets. [Mandelbrot, "Fractals," 1977]
The term was suggested earlier in Mandelbrot's 1967 book, "How Long is the Coast of Britain -- Statistical Self-Similarity and Fractional Dimension."
Proto-Indo-European root meaning "to break."
It forms all or part of: anfractuous; Brabant; bracken; brake (n.1) "stopping device for a wheel;" brake (n.2) "kind of fern;" brash; breach; break; breccia; breeches; brioche; chamfer; defray; diffraction; fractal; fraction; fractious; fracture; fragile; fragility; fragment; frail; frangible; infraction; infringe; irrefragable; irrefrangible; naufragous; ossifrage; refract; refraction; refrain (n.); refrangible; sassafras; saxifrage; suffragan; suffrage.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit (giri)-bhraj "breaking-forth (out of the mountains);" Latin frangere "to break (something) in pieces, shatter, fracture;" Lithuanian braškėti "crash, crack;" Old Irish braigim "break wind;" Gothic brikan, Old English brecan "to break."