The ProjeKcts were most active from 1997 to 1999, but have performed intermittently since. These earlier ProjeKcts, up to ProjeKct Six in 2006, were devoted to instrumental and heavily improvised music. All of them included King Crimson guitarist Robert Fripp, who described their purpose as being "research and development" for King Crimson. Two later spin-off projects were of a different nature, but both involving former King Crimson members.
ProjeKct One began as a suggestion by Bruford to Robert Fripp that they do some improvisational shows together. Fripp suggested adding Gunn, while Bruford suggested adding Tony Levin — four of the six members of King Crimson were now involved.
Fripp then developed the idea of "fraKctals": multiple different subsets of the band working separately as a way of developing new material for King Crimson, the band having been at something of a compositional impasse.