Biolistic Gene Gun: Particle Bombardment Transformation (2D)

This 2D counterpart to the biolistics gene-gun simulator renders a plant-tissue cross section as a row of cells, each with its own nucleus depth. DNA-coated gold microcarriers are fired straight down under a real quadratic-drag ODE — the same physics as the 3D version — and each cell's outcome is decided by the particle's velocity right at the nucleus: too slow and it never arrives (failed transformation), too fast and it ruptures the cell (dead), and only a narrow "Goldilocks" band of impact velocity and particle size delivers DNA without killing the cell (successful transformation). A live sweep chart re-integrates the same ODE across the whole velocity range and plots the success rate, so the narrow optimal-velocity peak — and how it shifts and narrows with particle diameter — is directly visible and numerically verifiable, not just implied by the animation.