Black Hole Vision vs Wyrm Math

What would the world around you look like if you were staring at a black hole? This application places a black hole in the field of view of your iPhone’s camera and gravitationally "lenses" the resulting live video feeds just as a black hole would warp the light from surrounding stars. The resulting "Black Hole Vision" reveals interesting features of black hole lensing, including a "photon ring" of strongly lensed images around the black hole. The measurement of this photon ring will be the target of future astronomical observations from space with the Black Hole Explorer: an orbit satellite that will take the sharpest images in the history of astronomy! To learn more about BHEX, head over to https://www.blackholeexplorer.org/. The code is open source and freely available on GitHub at https://github.com/graveltr/BlackHoleVision, along with documentation that explains the underlying black hole lensing equations and how they are implemented in Black Hole Vision. The code was written at Vanderbilt University by Trevor Gravely with input from Dr. Roman Berens and Prof. Alex Lupsasca. We also acknowledge Dominic Chang for useful input and comments. This project was supported by CAREER award PHY-2340457 and grant AST-2307888 from the National Science Foundation. The lensed image of the spiral galaxy Messier 101 was generated using material produced by NASA and STScI and can be found here: https://hubblesite.org/contents/media/images/2006/10/1865-Image.html?news=true. License: This app includes a port of the GNU Scientific Library's (GSL) implementation of Jacobi elliptic functions and the elliptic integrals to Metal. It is licensed under the GNU General Public License v3.0 (GPL-3.0). You can view the full license and obtain a copy of the source code at: https://github.com/graveltr/BlackHoleVision.

Wyrm Math turns algebra into something you do with your hands. Instead of typing commands or watching a video, you solve equations by direct touch — drag a term across the equals sign and it flips sign, pull a factor apart, split a fraction. The equation responds to your gestures in real time. The difference: Wyrm only ever lets you make legal moves. Every change goes through a real math engine, so an illegal step simply isn't possible. You can't break the math — which means you're free to experiment, and what you learn is the actual structure of algebra, not a set of memorized tricks. WHAT YOU CAN DO - Solve by dragging — move terms, factor, distribute, cancel, and split fractions with your fingers - Play the campaign — a star-rated game mode that dares you to solve in as few moves as possible - See every step — a running derivation you can scroll back through and learn from - Track the fine print — when a move depends on a condition (like a denominator ≠ 0), Wyrm shows it as an assumption you can tap to trace - Get unstuck — "Guide me" coaches you toward the next legal move without doing it for you - Explore freely — try a "what-if," check your solution, or back up and take a different path GAME MODE — BEAT PAR Game mode is an algebra game with a score. Every equation has a par: the fewest moves it takes to solve. You get a fresh problem, your moves are counted, and the solve is rated against par — three stars if you match it. Seven stages climb from one-step equations through variables on both sides, distribution, fractions, and powers to quadratics, each with its own colors and sound. Earn enough stars to advance; beat par and you bank an undo token to spend on a harder problem later. There's no coaching and no free undo here — you already know your moves are legal. The only challenge is finding the shortest path. Unlike most math games, the notation is real and so is the algebra. FROM FIRST EQUATIONS TO REAL ALGEBRA Start with one-step equations like x + 2 = 5 and work all the way up to multi-step linear equations and the quadratic formula. Wyrm grows with you. BUILT FOR LEARNING BY DOING Whether you're a student trying to actually understand algebra, a parent helping with homework, or anyone who wants to rebuild their math intuition, Wyrm replaces "follow these steps" with "try it and see why it works." No accounts. No ads. No data collection. Just you and the math.