N / Squares

Interactive study · layers & phase

A different point of view.

Stack the phase slices of a Naglich Square. Color makes repeated values visible; spacing gives each layer room to breathe.

Named TLF seed · isometric study

One family, many slices.

Isometric stack of TLF phase slicesA configurable geometric view of the numeric grids.

Shape your view

What you are seeing

Color is a reading aid.

Each tile is a cell at a row and column. Each layer is one phase k; phases wrap from N back to 1. Changing the palette, spacing or viewing direction changes the display, not the values. Emphasis fades other values without removing their cells.

This SVG study uses four fixed isometric viewpoints. It shows arithmetic phase layers, with no free orbit or physical simulation. Overlapping layers can obscure cells; reduce the layer count or open the numeric explorer for exact inspection.

One explicit convention

All coordinates are 1-indexed. This study uses the named TLF seed:

A(r,c,k,N) = ((r − 1) · wrapN(c − 1,N) + k − 1) mod N + 1

Here wrapN(x,N) = ((x − 1) mod N) + 1, using a nonnegative remainder. It is one declared seed, not a claim that every historical viewer uses the same convention.

Inspect the exact numeric grid →
Read the family conventions →

A separate 3D study

The advanced legacy k-slice viewer offers WebGL layers, formula comparison, presets and export controls. It uses its own conventions; this page studies the named TLF phase stack.

The legacy viewer’s required 3D libraries are bundled locally. Its rendering and export review remains separate from this page’s mathematical study. See Guides & archive for instrument review notes.