Infinomatic vs p

Explore infinity with Infinomatic — a powerful engine for discovering the beauty of fractal systems. Navigate the Mandelbrot set in real time, zoom deep into intricate structures, and select any point to reveal its corresponding Julia set. Every location opens a new world of patterns, symmetry, and unexpected detail. Features: • Real-time Mandelbrot and Julia rendering • Smooth, responsive deep-zoom navigation • Live Julia previews from selected Mandelbrot points • Automatic guided zoom for continuous exploration • Curated presets and personal bookmarks • Multiple colour palettes, including a colourblind-safe option • Adaptive rendering for smooth performance • Full-quality image sharing • Educational content explaining the mathematics behind fractals • Precision warnings at extreme zoom levels Built with Metal for high-performance rendering on iPhone and iPad, Infinomatic transforms complex mathematics into an intuitive visual journey. Zoom in. Explore deeper. Discover the infinite.

p-adelic shows a number in all of its completions at once. Type 1/3, √2, a polynomial or log 7 and watch the adelic strip: one column for the real line and one for each prime p, each streaming the number's digits in base p and growing leftward as you turn the precision dial. There is no "p-adic mode" to switch into — you always see the whole picture, the way number theorists think about it. THE STRIP • A column per place: ∞ plus the primes that matter for your input, and any prime you pin. • Streaming precision from 5 to 200 digits; every column updates together. • Exact periodicity for rationals: the repeating block is marked with an overline, and long runs of digits fold into pills you can tap open. • Tap a column to focus it; the focused card shows valuations, unit parts, Legendre symbols and the Laurent form. DEEP DIVE • Digits, Laurent series and Witt-vector views of the same number. • Nested balls: zoom into ℤₚ ball by ball, following your number's digits. • The Bruhat–Tits tree and the Berkovich line of the chosen place. ALGEBRAIC NUMBERS • √d, roots of unity ζₙ, Teichmüller representatives, and any algebraic number given by its minimal polynomial, e.g. algebraic(x³ − 2). • See whether a prime splits, stays inert or ramifies; extend the field with one tap and cycle through the Galois conjugates. POLYNOMIALS • Newton polygons at every prime and at ∞, with slopes, multiplicities and the Krasner check. SPECIAL FUNCTIONS • p-adic exp, log and Artin–Hasse, with their convergence disks. • Factorials with Legendre's formula, Morita's Γₚ with the Wilson check. • Kubota–Leopoldt ζₚ and L-values, Hilbert symbols with the reciprocity check, and Tate's local factors. LEARN AND REUSE • A Library of worked examples for every idea above, from −1 = …(p−1)(p−1)(p−1) to the Berkovich line of ∛2. • History you can reopen with one tap. • VoiceOver describes every visualization; text and digits follow Dynamic Type. PRIVATE BY DESIGN Everything is computed on your device. The app has no account, no analytics and makes no network connections. For students meeting p-adic numbers for the first time, teachers who want a live picture to point at, and researchers who need a Newton polygon or a Hilbert symbol checked in seconds.