  Synthesis of ergodic, stationary visual patterns is widely applicable in
texturing, shape modeling, and digital content creation. The wide applicability
of this technique thus requires the pattern synthesis approaches to be
scalable, diverse, and authentic. In this paper, we propose an exemplar-based
visual pattern synthesis framework that aims to model the inner statistics of
visual patterns and generate new, versatile patterns that meet the
aforementioned requirements. To this end, we propose an implicit network based
on generative adversarial network (GAN) and periodic encoding, thus calling our
network the Implicit Periodic Field Network (IPFN). The design of IPFN ensures
scalability: the implicit formulation directly maps the input coordinates to
features, which enables synthesis of arbitrary size and is computationally
efficient for 3D shape synthesis. Learning with a periodic encoding scheme
encourages diversity: the network is constrained to model the inner statistics
of the exemplar based on spatial latent codes in a periodic field. Coupled with
continuously designed GAN training procedures, IPFN is shown to synthesize
tileable patterns with smooth transitions and local variations. Last but not
least, thanks to both the adversarial training technique and the encoded
Fourier features, IPFN learns high-frequency functions that produce authentic,
high-quality results. To validate our approach, we present novel experimental
results on various applications in 2D texture synthesis and 3D shape synthesis.
