<p>Offset boosting is the essential channel for attractor distribution control in phase space. Two-dimensional offset boosting brings great potential for attractor regulation, where a single periodic function contains hidden synchronous offset shift leading to diagonal attractor self-reproducing in phase space. In this work, the mechanism of diagonal attractor self-reproducing is analyzed, where multiple-dimensional offset boosting reduces the number of periodic functions for attractor reproduction. Bifurcation and non-bifurcation parameters are applied for attractor distribution control, including the size, types and distribution of coexisting attractors. Furthermore, the diagonal attractor self-reproducing can also be coined in higher-dimensional space or in those systems with complex nonlinear feedback if the interlocked linear feedback is preserved. Diagonal attractor self-reproducing brings great convenience for multistability design and for high-dimensional chaos regulation.</p>