Fibonacci anyon vs Rondo

This app introduces the fusion channels of Fibonacci anyons. You can have some understanding for the fusion of Fibonacci anyons.

Rondo turns the counting numbers into a quiet, hypnotic dance. Every number from 1 upward is drawn as a factorization diagram: nested rings of colored dots that show, at a glance, how that number is built from its prime factors. 6 is two groups of three. 12 is three groups of four. Primes can't be split, so they shimmer alone. Then the diagram melts and re-forms into the next number, and the next, an endless looping dance of arithmetic. It's equal parts math toy, teaching tool, and ambient art. WATCH, OR EXPLORE • Let it play for a calm, continuous dance from one number to the next • Tap to pause, drag to scrub to any number, or step one at a time • Speed it up, or slow it right down • A gentle haptic tap each time the dance lands on a prime • Follow any number down its Collatz orbit, and watch it fall back to 1 HEAR IT • Every number sings its factorization: a prime is a single pure tone, a composite a chord of its prime factors • On by default, off whenever you like POINT YOUR CAMERA • Aim Rondo at any printed number and watch its diagram bloom over the page, in augmented reality • Lift a number's diagram off the page and into the room, then walk around it • Street signs, receipts, book pages: factor the world around you EVERY NUMBER HAS A STORY • Tap any number to see what makes it special: whether it's prime, a perfect number, a power, and more • Collect the special numbers you find in the Field Guide SEE THE MATH • The current number and its factorization, always in view • Full VoiceOver support and a spoken read-out of each number and how it factors • Save the numbers you love to Favorites, and share any diagram as an image ON YOUR HOME SCREEN AND WRIST • Widgets that turn today's date into factorization diagrams, across the Home Screen, Lock Screen, and StandBy • A factorization calendar for the month or the current week • A widget for a number you pin, and a stepper widget you tap to walk one number at a time • An Apple Watch app: scrub through the numbers with the Digital Crown, with the same prime haptics • Ask Siri for a number, or add Rondo to a Shortcut • An optional nudge on days whose number is itself worth a look MAKE IT YOURS WITH RONDO PRO A one-time unlock, never a subscription. The full dance stays free. Pro is for going deeper: • New color palettes, backgrounds, and color styles • Layout options for how the rings nest and order themselves • A living clock face that factors the time • Number sequences: count by multiples, primes only, Fibonacci, and more • The full instrument: tune the scale, voice, and space of the sound • Hear any number's story narrated aloud, in your choice of tone CALM BY DESIGN No ads. No tracking. No account. No subscription. Rondo is free to play, with an optional one-time Pro unlock. A LOVING HOMAGE Rondo is a faithful tribute to Brent Yorgey's factorization diagrams and Stephen Von Worley's animated "Factor Conga," built natively for iPhone, iPad, and Apple Watch. The diagrams honor their work; the sound, the augmented reality, and the stories are Rondo's own. Full credits are in the app.