A run of numbers laid onto a shape.
MAYAN ALFA V1008 takes a run with a period of 260, lays it onto a chosen surface or solid, and computes tables, matrices and layers from it. All in a single HTML file, with no installation and no server.
What it is
One HTML file. Open it in a browser and it runs — no installation, no server, no sign-up. It draws to a canvas, and the interface is in both Czech and English.
At its base is the run: ρ(i) by the chosen law, a period of 260, mirrored every cycle. Branch REV is the mirror of branch P, and a fixed identity holds between them.
Primes come from a sieve of Eratosthenes up to 100,000, with a sieve window for a starting n₀ as high as 100,000,000.
Eleven scenes, each one click away
Every scene sets the law, the surface, the drawing, the view and which windows open. They are also the fastest way to find out what the tool can do.
1 · KROK on the torus
The basic V1008 law on the torus R=150, r=130. Lines along the shell, points and primes, a slow turn — this is what the run looks like with nothing hidden.
2 · Sphere · LOG2FYZ
A logarithm with a physical profile on a sphere, the golden angle 137.508° instead of 18.45°. The points never line up into rays.
3 · Formula ρ(i) and Δφ(i)
Your own law written as an expression: ρ runs on a cosine at three times the frequency, the angle grows with distance from the centre.
4 · Hexagonal plan
The surface of revolution gets a hexagonal plan. The tables are computed from the real plan, so segments and bins rearrange.
5 · Branch P · spiral vortices
Only branch P and the angle 360/√2 = 254.558°. An irrational ratio to a full turn produces counter-rotating vortices that never close.
6 · Segmentation and ANGLE
The Segments ρ and ANGLE tables next to the image. Clicking a cell marks those points on the object — you can see what goes into which bucket.
7 · Matrix and Dirichlet
The segment × BIN matrix and a highlighted class n ≡ a (mod 12). The primes of that class turn white and you can see where they run on the shell.
8 · A formula on a star
The small stellated dodecahedron with a custom ρ(i) on a square root. The mapping is turned onto a vertex, so the run heads straight into a spike.
9 · RH and gaps
The ζ · RH · L window with the run's path in the s-plane, the RH/GRH band and the prime-gap matrix. The points in the image are coloured by ζ.
10 · Classic Ulam
The infinite surface: the run is laid into a square spiral by n and only primes are marked. 250,000 numbers, every prime, nothing thinned.
11 · Tokamak — simulation on a replica
The V1008 law laid onto the ITER plasma: Miller D, branch P along the upper half, REV along the lower, a 120° cutaway between the 18 TF coils looks inside.
What it does
The interface is assembled from windows and columns you switch on as needed. Here is what's in the tool.
- KROK, COS, LOG, LOG2FYZ — the V1008 laws
- SIN, TAN, COTG — trigonometric
- SQRT, KVAD, HARM — power and harmonic
- ULMA (Ulam rings) and V4 as a reference model
- Angular step of 18.45°, a custom angle, or an angle from a formula
- Your own ρ(i) and Δφ(i) written as expressions
- A library of 62 ready-made formulas
- Adjustments: smooth, symmetrise, uniform time
- Five ways of handling points that fall outside the range
- Torus (R=150, r=130), sphere, torus → sphere morph, Möbius strip, φ × ρ map
- Infinite surface developed by n; Ulam, Sacks, Vogel, spiral
- Spheroid, superellipsoid, Flamm paraboloid, hyperboloid, catenoid ↔ helicoid
- Klein bottle, Clifford torus on S³ (Hopf), tube around a torus knot (p, q)
- Nine groups of solids: Platonic, their pairs including in the golden ratio, Kepler, Poinsot, Archimedean, truncated, quasiregular and Catalan
- Mapping by the V1008 axes or onto a chosen vertex of the solid
- Circular or polygonal plan, stepped profile, adjustable torus diameters
- 20 ρ bands and 20 bins of 18°
- Computed from the actual plan of the current surface, not from the law's values
- Clicking a cell marks the corresponding points on the object itself
- Segment × BIN matrix and twin matrix, 20 × 20
- A cell selection carries through to the image and to the ρ band
- 004 Gaps — sector × gap, Gaussian layer, gap matrix
- 005 Dirichlet → L(χ) — classes n ≡ a (mod q) and their link to L(s, χ)
- 009–012 — Z̄ pairs, RH equator, topology, ULMA rings
- The ζ · RH · L(χ) window: maps of ζ and L(s, χ), Hardy Z(t), the RH/GRH band, the run's path in the s-plane
- Colouring of points and surface by ζ
- Tensor — three matrices and their decomposition
- CSV P / REV import — load your own run
- Play the import back row by row and compare it with the torus
- PNG export of the image
- CSV export of the tables
- Save and load the whole configuration as JSON
- View bookmarks
- Colours, thicknesses, sizes, labels; the legend switches individual layers
- Appearance never touches the numbers — it only changes the image
- A description for each of the 369 interface items
- A strip at the bottom on hover and a full overview under „what is what“
- Keyboard shortcuts for views, focus, export and starting the run
The TOKAMAK module
The surface switches to a D cross-section using the Miller parametrisation: major radius R₀, minor radius a, elongation κ and triangularity δ set separately for the upper and lower half. Add the number of TF coils, a cutaway to look inside, the vacuum vessel, and binding of ρ to the plasma edge or to a flux surface.
The replicas are parametrised from real machines. The values are indicative, accurate to a tenth; the TF coil count for GOLEM is an estimate.
The Dynamics window
- Categories: field lines, particles, MHD events, waves, plasma
- Larmor radius, banana width and island width as a reach tube around the path
- A glow along the curve, a comet at the head with a fading trail, sparks at the cycle boundary
- The flux surface the head is currently on, highlighted
- Worked cases set the formula, the run, the drawing, the view and the dynamics
- TOKAMAK DEMO — partial presets for the replica, cutaway, layers, plasma profile and passage of time
What holds and doesn't change
This is the part that makes the results trustworthy. It applies whatever surface or appearance you choose.
- The branch identity ρ_P + ρ_REV = 2R holds on every geometry
- The period of 260, the 18° binning and the 20 ρ segments don't change with surface or appearance
- Tables and primes are computed from ALL points of the run — drawing density and layers change only the image
- Your own formula changes the law, not the measurement: bins and segmentation stay put
Good to know in advance
I'd rather say this myself than have you run into it mid-task.
- The run law is chosen first — tables and layers are computed from it.
- Tables are computed from branch P; REV is drawn as its mirror.
- ζ and the tensor compute on the main thread. Expect a short lag when you switch them on — you can avoid it by turning off „compute sums“, and the image then runs faster.
- Drawing goes to a CPU canvas, not WebGL. With hundreds of thousands of segments, you notice.
- The help text is currently Czech only, though the interface itself is bilingual.
- This is a viewer and a laboratory, not a proof system. The ζ · RH · L(χ) window is a map and a visualisation — it proves nothing.
Licence
You get the whole HTML file. It's readable and editable — that is the source code. The licence runs for one year from purchase and is then renewed.
You may modify it
Open the file and change it. Add a layer, change the law, adapt it to your data.
You may use it for your work
Commercially or not, on your own projects, with no cap on the number of runs.
A one-year licence
Valid for 12 months from purchase. It renews after a year; without renewal, updates and support end.
You may not redistribute it
You may not pass on, sell or otherwise make the file or modified versions of it available to third parties.
Editions
An annual licence. Fill in prices according to how you want to sell it.
Full
- All 11 scenes and every module
- CSV P / REV import
- PNG, CSV and JSON export
- The whole file, with the right to modify
- Updates throughout the licence year
Institutional
- Multi-user licence
- Custom modifications
- Consultation on deployment
- Renewal on an agreed cycle
Want to see it running?
Tell me what you'd like to put through it — your own run as CSV, a particular surface, a particular replica. If the tool can't do it, I'll say so straight away.