Simulating Differential Equations Using FPGA Boards

Summary

This project addresses the challenge of visualizing and interacting with chaotic systems—such as the Lorenz attractor and mass-spring-damper models—by implementing them in real time on hardware. The core objective is to design a high-speed numerical engine using a Field Programmable Gate Array (FPGA) that solves ordinary differential equations (ODEs) at tens of thousands of steps per second. By enabling live parameter tuning, users can dynamically adjust system variables like damping, stiffness, and nonlinear coefficients, instantly observing the effects through various output interfaces including oscilloscopes, VGA displays, and hardware-in-the-loop setups.

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