Recursive computation of Feynman periods

Feynman periods are integrals that do not depend on external kinematics. Their computation, which is necessary for many applications of quantum field theory, greatly facilitated by graphical functions or the equivalent conformal four-point integrals. We describe a set transformation rules act such and allow their recursive computation in arbitrary even dimensions. As concrete example we compute all subdivergence-free $\phi^3$ theory up to six loops 561 607 at seven loops. Our results support conjectured existence coaction structure suggest $\phi^4$ share same number content.