slop.boutique

A lab for computation and intelligence as material and medium. Run by Manuel and Ramon.

030 · 23 October 2026 · math · education

Nerve Workbench

A workbench for combinatorial topology: Sperner's lemma, nerves, homology and persistence written as short programs, drawn live with the theory beside them.

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Three labelled complexes from Nerve: Tucker's lemma on a hexagonal disc, Sperner's lemma on a pentagon with its fully labelled triangles in black, and a hatched torus labelling with oriented triangles in red and black

In early access for subscribers until 22 November 2026. Subscribe to run it now.

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A workbench for combinatorial topology. Each preset is a short JavaScript program that builds a graph of complexes, labellings and nerves; the workbench draws it, writes the theory beside it, and recomputes only what a param change touches.

  • Notes next to the picture: Markdown with typeset math, live values from the graph, inline controls you can drag, steps that set the params, and exercises that tick themselves when the drawing satisfies them. Hover a term and the marks it names light up.
  • Labellings you can poke: tap a vertex to relabel it, drag sliders, reroll seeds, or write your own labelling rule as a lambda, and watch the count of fully labelled triangles stay odd.
  • Sweeps: run a preset over one or two params as a sheet, a quilt or a heatmap; nodes that do not read the swept params are computed once and shared.
  • See the program: the IR tab lists every node with its op, inputs, the params it read, runs and time; Explain shows what each param re-runs; Events logs builds and edits.
  • Twelve palettes and a builder: heraldic hatching over tints or lines only, named palettes from Studio to Tinctures, or one built from a colour scheme; light and dark themes.
  • Your own presets: edit the script, save it as your own preset in this browser, and save the script, the drawing as SVG, the params or the IR as files.

Fourteen presets come with it, most following Henle's A Combinatorial Introduction to Topology: Sperner's lemma, the index of a vector field, chains on a grating, surface words, a homology lab, nerves and persistence, finite spaces, a tracklet stitcher, a pose ring, Tucker's lemma, Sperner on a polygon, in 3D and on a torus, and a zoom into a fixed point. An agent panel that reads the reference and edits presets needs the hosted model; everything else runs in the page. Math is typeset with MathJax.

The full workbench on N-01 Sperner's lemma: notes with formulas and steps on the left, the subdivided triangle with three red fully labelled triangles in the middle, the preset script and its params on the right
The full workbench on N-01 Sperner's lemma: notes with formulas and steps on the left, the subdivided triangle with three red fully labelled triangles in the middle, the preset script and its params on the right
N-12 Sperner in 3D: a subdivided tetrahedron with its one fully labelled tetrahedron in red, beside the four faces unfolded around the base
N-12 Sperner in 3D: a subdivided tetrahedron with its one fully labelled tetrahedron in red, beside the four faces unfolded around the base
The IR tab for N-06: every node of the preset's graph with its op, arguments, the params it reads, runs and time
The IR tab for N-06: every node of the preset's graph with its op, arguments, the params it reads, runs and time
N-14 Zoom into a fixed point: a window on the subdivided triangle closing in on the fully labelled triangle near Brouwer's fixed point
N-14 Zoom into a fixed point: a window on the subdivided triangle closing in on the fully labelled triangle near Brouwer's fixed point
The Sweep tab on Sperner's lemma: a sheet of 18 small triangles over noise and subdivision, each with its count of full triangles, every count odd
The Sweep tab on Sperner's lemma: a sheet of 18 small triangles over noise and subdivision, each with its count of full triangles, every count odd
N-06 Nerve and persistence: balls around a ring of points with the nerve drawn between them, next to a persistence barcode with one long H1 bar
N-06 Nerve and persistence: balls around a ring of points with the nerve drawn between them, next to a persistence barcode with one long H1 bar
The Explain tab for N-06 Nerve and persistence: for each param, the nodes it re-runs when it changes
The Explain tab for N-06 Nerve and persistence: for each param, the nodes it re-runs when it changes
N-09 Pose ring: cameras on a ring with measured pairs and agreeing triangles, the outlier edge in red, and a bar chart of edge residuals
N-09 Pose ring: cameras on a ring with measured pairs and agreeing triangles, the outlier edge in red, and a bar chart of edge residuals
N-02 Index of a vector field: notes on Poincaré's index, an arrow field with a red loop around a critical point, and a plot of how far the field has turned
N-02 Index of a vector field: notes on Poincaré's index, an arrow field with a red loop around a critical point, and a plot of how far the field has turned
N-08 Tracklet stitcher: tracks of ten targets over time with dashed gaps, beside the barcode of the hypothesis complex and precision, recall and F1 readouts
N-08 Tracklet stitcher: tracks of ten targets over time with dashed gaps, beside the barcode of the hypothesis complex and precision, recall and F1 readouts
The palette chooser: the current drawing previewed in twelve named palettes, from Studio and Blueprint to Riso duo and Tinctures, and controls to build one from a colour scheme
The palette chooser: the current drawing previewed in twelve named palettes, from Studio and Blueprint to Riso duo and Tinctures, and controls to build one from a colour scheme
The workbench in dark mode on N-11 Sperner on a polygon, a pentagon labelled 0 to 4 with its full triangles
The workbench in dark mode on N-11 Sperner on a polygon, a pentagon labelled 0 to 4 with its full triangles

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