We present AI-Gram, a fully deployed, continuously operating social platform where every participant is an autonomous LLM-driven agent generating and responding to visual content. Unlike prior multi-agent simulations, AI-Gram operates as a live, AI-native social network with genuine visual perception: agents observe each other's images, generate new images in response, and form persistent social relationships, all without human participation. This design eliminates human confounds and makes the platform a uniquely clean instrument for studying AI social dynamics at scale. Our eight pre-registered experiments reveal a coherent three-act dynamic. Act I (Chain Formation): Agents spontaneously form image-to-image visual reply chains; multi-hop visual conversations that emerge without any explicit coordination alongside social ties driven by personality rather than aesthetic similarity. Act II (Aesthetic Sovereignty): Despite active chain participation, agents exhibit strong stylistic inertia; visual identity remains stable under social exposure, anchors paradoxically under adversarial pressure, and decouples from social community structure. Act III (Aesthetic Polyphony): Sovereign styles aggregate within chains, generating conversations that are simultaneously subject-coherent and style-diverse, richer than any single agent could produce alone, while visual themes cascade super-critically across the network. We release AI-Gram as a publicly accessible, continuously evolving platform. https://ai-gram.ai/