Where Numbers Become Windows Into Hidden Patterns
Enter a universe where numbers wrap instead of run away, where prime factors form lattices, and modular arithmetic unveils living holograms. Naglich Squares (NS8) are more than math—they’re a gateway into art, physics, music, and code.
🔹 Explore the Grids – Watch each size N reveal unique star-like windows shaped by modular patterns and prime factors.
🔹 Learn the Theory – See how simple number cascades create structured holographic order.
🔹 Experiment & Create – Transform NS8 into visuals, sound, and interactive tools that bridge science, math, and art.
Tools / Demos
Interactive Heatmap & k-Sequence
Interactive Heatmap & k-Sequence An interactive, mobile-friendly explorer for Naglich Squares. It renders an N×N heatmap for any size N (1–72) and key k (1..N), and lets you animate k, inspect values on hover, and highlight patterns (1-4-7 / 2-5-8 / 3-6-9, primes, evens/odds, or your own set). The canvas is HiDPI-crisp with a fit-to-canvas… Interactive Heatmap & k-Sequence
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Beat Explorer
Naglich Squares — Beat Explorer v7 (Responsive + Theme) Naglich Squares — Beat Explorer v7 N Checking… k b(v) = N / gcd(N, v−k) Timeline steps Show values per beat Prime‑factor view ▶ Play BPM Global click Per‑lane clicks Vol LCM overlay Residue overlay (t mod d) Column heatmap Polyrhythm Timeline Autocorrelation (coincidence sequence) Column… Beat Explorer
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Simple QCA Lab
nsquares | QCA Lab — Naglich Squares nsquares | QCA Lab Reversible, translation‑invariant, local‑unitary update rules derived from the Naglich Squares orientation family. Optimized dark UI, responsive for desktop, tablet, and mobile. Controls N=283 • Prime N 283 k 11 Steps 0 Renderer Canvas 2DWebGL (beta) Run FPS Max6030155 Quality AutoHighBalancedUltra‑fast World TiledSingle tile Palette… Simple QCA Lab
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3D k Slice Viewer
3D k-Stack Viewer An interactive, mobile-friendly playground for exploring Naglich Squares in 3D. Each layer (k = 1..N) renders an N×N grid where cells are colored by the value ofM[r,c] = ((r·c + (k−1)) mod N) + 1. Layers stack in depth so you can orbit, slice, and spot symmetries at a glance. Try it… 3D k Slice Viewer
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Naglich Square RL/LR Algorithmic Grids
RL/LR Algorithmic Grids — Math Modes + Animation RL/LR Algorithmic Grids Tabbed controls • Product math by default • Animate k or N • Filter & export PNG/GIF/WebM/MP4. Share state Reset Controls N = 9 k = 9 Composite N k Basics Palettes & Filters Export & Animation Grid size N N = 9 Variant… Naglich Square RL/LR Algorithmic Grids
Load ToolBlog / White Papers
Windows in the Lattice: Why NS8 Splits Into Tiles
Abstract If you’ve ever rendered an NS8 star lattice across many values of NNN, you’ve probably noticed something striking: the lattice doesn’t just get sharper as N increases — it splits into windows. These look like 2×2, 3×3, 4×4, or larger blocks, repeating across the grid. Some are crisp and obvious, while others are subtle or… Windows in the Lattice: Why NS8 Splits Into Tiles
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NS8 vs. a Regular Multiplication Table
Abstract When you first encounter NS8 (Naglich Squares), it might look like just another multiplication table. But the two are very different in how they behave, what they reveal, and the kinds of patterns they expose. Here’s a breakdown. 1. Output Range Multiplication table: Entries grow without bound. A cell at row r and column… NS8 vs. a Regular Multiplication Table
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From Number Cascades to the Vision of a Holographic Ternary Computer
Abstract This paper presents a theoretical framework for understanding Naglich Squares: two-dimensional number lattices generated from cascading sequences. Beginning from the premise of nothingness giving rise to one, and one unfolding into two, three, and beyond, we trace how numbers form cascades of order that naturally expand into structured grids. These grids — the Naglich… From Number Cascades to the Vision of a Holographic Ternary Computer
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Naglich Squares — Forward/Backward Family
Naglich Squares — Forward/Backward White-Paper Demo Naglich Squares — Forward/Backward Family History & naming, arithmetic formulas, QCA context, and colorized grids for each orientation. All indices are 1-based. History Naming Formulas Legend & Controls Forward Demos Backward Demos Quantum Cellular Automata Uses & Further Research Research & Future Work History (short) Naglich Squares are RL-style… Naglich Squares — Forward/Backward Family
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