Jones polynomial vs Deltarium

This app introduces Jones polynomial. You can have some understanding for Jones polynomial.

Deltarium is a place to walk among worlds, the way a planetarium is a place to walk among stars. Each world is a living system of change. You move a few sliders, press play, and watch what the mathematics does: rabbits and foxes chase each other in cycles, a chaotic attractor traces its butterfly wings, a rocket bends time on its way to another star. Built for kids and curious people first, and for scientists too. There is nothing to sign into, nothing to buy, and no ads. The app runs entirely on your phone and collects nothing. THE 8 WORLDS PREDATOR AND PREY. The classic hare-and-lynx cycle. Set the birth, hunting, and dying rates and watch the populations chase each other around a loop. A guided tour walks through this world one step at a time. THE BUTTERFLY. The Lorenz attractor in 3D, spun with a finger. Turn on the twin path, which starts a hair away from the first, and watch the two separate. The butterfly effect you can see. ESTUARY. A coastal model of nutrients and life that blooms and crashes with the seasons. THE DANCE. Three stars pulling on each other, including the famous figure-eight where they chase one another forever. PARKING IN SPACE. The 5 Lagrange points, the spots where a small craft can hold its place relative to the Earth and Moon. Give all 5 a shared kick and see which ones stay parked and which wander off. RADIOACTIVITY. How a radioactive source fades over time, following the real decay chain from a parent down through its daughters. TIME DILATION. A rocket that holds a steady 1 gravity of thrust all the way to a distant star, flipping over at the midpoint to slow down. The clock on the ship and the clock back on Earth pull apart. BUILD YOUR OWN. Write your own equations, add sliders for the parts you want to tune, and watch the system run. UNDER THE HOOD Every world is a real system of ordinary differential equations, solved on your phone by the same numerical method scientists use. Each screen carries a science card naming the model, its author, and a reference you can look up. The phone's engine is checked against a published Python reference, and all the source code is public at github.com/evanleeturner/deltarium-iphone.