Eternal AI: Recursive Self-Improvement Curve

This simulation investigates the long-term implications of an eternal artificial intelligence — one whose own capability continuously feeds back into its own growth, in principle without end. Rather than an abstract animation, it grounds that idea in a real dynamical-systems model: capability C(t) evolves under dC/dt = k·C^p·(1−C/R), a resource-capped recursive-growth equation drawn from the AI-safety "intelligence explosion" literature. A branching 3D cognition network expands outward as capability grows, giving a direct visual read on the difference between a system that plateaus, one that grows smoothly exponential, and one that takes off explosively before its compute ceiling catches it. Three sliders — feedback strength, growth exponent and compute ceiling — let you explore the whole space of takeoff scenarios, from slow and self-limiting to fast and superlinear, while live readouts track capability, growth rate and how close the system is to its resource ceiling.