Pi vs FrackTell

Discover π like never before. Pi — Infinite Digits lets you calculate any decimal of the mathematical constant π with absolute precision. Whether you're a student, a mathematician, or simply curious, this app gives you access to the infinite digits of π directly on your iPhone. Two powerful modes: First N digits — Display the first N decimal digits of π, from 1 to 50,000 locally, and beyond via the internet. Nth digit — Find exactly which digit appears at any position in π. What is the 1,000,000th decimal? Find out in milliseconds. Unmatched precision: Pi uses the Chudnovsky algorithm, one of the fastest known methods for computing π, combined with arbitrary-precision arithmetic (BigInt). Every digit is mathematically exact — no floating point approximation, ever. For large numbers: Beyond 50,000 digits, Pi seamlessly connects to Google's pi.delivery API, giving you access to over 100 trillion decimal digits of π. The largest calculation ever made, right in your pocket. Features: Arbitrary precision up to 50,000 digits — fully offline Unlimited digits via internet (Google pi.delivery) Real-time progress bar with elapsed time Calculation history (last 5 results) Copy result to clipboard Export and share your results Clean, intuitive interface No ads, no subscriptions, no data collection Did you know? π (pi) is an irrational number — its decimals never repeat and never end. Mathematicians have computed over 100 trillion digits. Now you can explore them too.

Discover the infinite beauty of mathematics with FrackTell, the most advanced Mandelbrot set explorer for iOS. Journey into the depths of fractal geometry with unlimited zoom, stunning visualizations, and unique features that transform mathematics into art and music. INFINITE EXPLORATION Zoom forever into the Mandelbrot set with no practical limits. FrackTell intelligently switches between GPU-accelerated rendering for instant results and multi-core CPU processing with arbitrary precision for extreme zooms beyond 100 trillion times magnification. Every zoom level reveals completely new structures and patterns that never repeat. INTELLIGENT RENDERING - GPU Float Precision: Lightning-fast rendering up to 100x zoom - GPU Extended Precision: Crystal-clear quality up to 100 trillion times zoom - CPU Arbitrary Precision: Unlimited zoom with perfect mathematical accuracy - Adaptive iteration counts that scale with your zoom level for optimal detail - Real-time performance indicators show you which rendering mode is active CHAOS MUSIC Experience fractals through sound! Enable Chaos Music to hear the mathematical beauty around you. FrackTell continuously samples 16 points in a spiral pattern and converts iteration counts into musical notes using a pentatonic scale. Every location in the fractal produces a unique sonic signature that loops and updates as you explore. CHAOS ORACLE Let the fractal speak to you! Tap Speak Chaos to hear grammatically perfect sentences generated from your exact position, zoom level, and iteration count. The AI-powered Chaos Oracle uses your location as a seed to create unique philosophical insights and mystical observations. Every location generates different wisdom. JULIA SET DISCOVERY Every point in the Mandelbrot set has its own unique Julia set fractal! Long press anywhere to instantly view the corresponding Julia set. Points inside create connected island patterns, boundary points produce intricate fragmented fractals, and points outside create disconnected dust patterns. INTUITIVE CONTROLS - Pinch to zoom smoothly in and out - Drag to pan across the fractal landscape - Double-tap to zoom in 3x on any point with smooth animation - Long press to view Julia sets - Tap the palette button to cycle through 12 beautiful color schemes BEAUTIFUL VISUALIZATIONS - Smooth color gradients with adjustable hue shifts - 12 preset color palettes from cool blues to warm oranges - Real-time rendering with no lag during exploration - High-resolution export to save and share your discoveries - Dark mode optimized interface that lets the fractal shine EDUCATIONAL AND INFORMATIVE Learn about the mathematics behind the beauty with detailed information about what the Mandelbrot set is and why it is infinitely complex, how the simple equation creates infinite detail, the relationship between Mandelbrot and Julia sets, the history of fractal geometry, and how different rendering techniques work. POWERFUL FEATURES - Reset button to return to the full fractal view - Real-time zoom level display from 1x to trillions and beyond - Iteration count indicator shows computational complexity - Center coordinates display your exact location in the complex plane - Rendering mode indicator for GPU Float, GPU Extended, or CPU Arbitrary - Precision warnings when approaching hardware limits - Share your favorite discoveries with friends OPTIMIZED PERFORMANCE FrackTell is built with Metal for maximum GPU performance and multi-threaded CPU processing for extreme zooms. The app intelligently chooses the best rendering method for your zoom level, ensuring smooth performance whether you are at 10x or 10 quadrillion times magnification. PERFECT FOR - Mathematics enthusiasts and students - Fractal art lovers - Anyone curious about infinite complexity - Meditation and relaxation with chaos music - Teachers demonstrating mathematical concepts - Digital artists seeking inspiration