Foundations · a source-aware field guide
Marko Rodin
and Vortex Mathematics
A system where an old property of decimal arithmetic is drawn as motion, wound into hardware, and interpreted as a map of the universe. This page keeps the pattern, the machine, and the claims visible without pretending they are the same kind of evidence.
The source: a diagram that became a worldview
Marko Rodin developed and popularized what he calls Vortex-Based Mathematics: a way of arranging the digits 1 through 9 around a circle, tracing recurring digital-root sequences, and reading the resulting paths as a toroidal model of energy and form.
There is no single, stable scholarly edition that cleanly separates Rodin’s earliest presentations from later teaching, community diagrams, and extensions by followers. That matters. Online material frequently blends Rodin’s language with later “vortex math,” free-energy, spiritual, and engineering claims. This page therefore attributes the broad system to Rodin while treating any more specific historical claim cautiously unless a dated primary source can be recovered.
The spelling used here is Marko Rodin, the form used in publications and Vortex-Based Mathematics materials. “Marco” is a common recollection and search variant.
The number map: what can be checked
A digital root repeatedly adds a number’s decimal digits until one digit remains. For example, 128 becomes 1 + 2 + 8 = 11, then 1 + 1 = 2. In base ten, this operation tracks a number modulo 9, with multiples of 9 represented by the digit 9 rather than 0.
digital root(n) = 1 + ((n − 1) mod 9), for n > 0Run the arithmetic
- Double 1 repeatedly: 1, 2, 4, 8, 16, 32, 64…
- Take each digital root: 1 → 2 → 4 → 8 → 7 → 5 → 1.
- Double 3 repeatedly and reduce: 3 → 6 → 3 → 6.
- Multiples of 9 reduce to 9.
This is why the diagram is compelling: a simple operation produces stable, visible cycles. It is also base-dependent. In another numeral base, digit sums reduce modulo one less than that base, so the special role of 9 here comes from decimal notation.
The coil: when the diagram becomes hardware
A Rodin-style coil winds conductive wire around a toroidal former in a crossing pattern inspired by the number map. Once current flows, it is an electromagnetic device governed by conductor geometry, current, frequency, resistance, inductance, capacitance, core material, and the surrounding space. Its field can be modeled and measured like that of other coils.
Two published laboratory studies are especially useful. A 2013 Review of Scientific Instruments paper described a twelve-sided Rodin coil used as the field source in a magnetic-stimulation device, recording frequency-dependent impedance, current, induced voltage, and magnetic-field intensity. A 2024 Revista Mexicana de Física paper modeled a simplified Rodin winding with the Biot–Savart law and finite elements, then compared the model with a three-axis Hall-sensor scan.
An evidence map: three different questions
Reproducible
Decimal cycles
Anyone can compute the digital roots and recover the 1-2-4-8-7-5 and 3-6 patterns. Standard modular arithmetic explains why they recur.
Measurable
Coil behavior
A specific winding can be built and its electrical response and magnetic field measured. Claims of unusual advantage require controlled comparisons with matched coils.
Unresolved
Universal interpretation
The diagram as a literal map of higher dimensions, consciousness, gravity, or an inexhaustible energy source remains an interpretive claim without decisive evidence.
| Claim | Current status | A useful test |
|---|---|---|
| The number cycles repeat. | Established for base-ten digital roots; explained by arithmetic modulo 9. | Repeat the calculation in bases 8, 10, 12, and 16 and compare which digit becomes the “return” value. |
| The winding creates a distinct field distribution. | Plausible and measurable; published models and scans exist. | Map a precisely documented Rodin winding and matched toroidal, solenoidal, and basket-wound controls at equal input power. |
| The winding is unusually efficient. | Not established by geometry alone. | Pre-register efficiency metrics; measure losses, Q factor, coupling, heating, and transferred power under identical conditions. |
| The 3-6-9 map reveals a fundamental law of nature. | Interpretive. The arithmetic’s dependence on numeral base is a major constraint. | Derive a quantitative, base-independent prediction that differs from standard theory and survives blinded replication. |
Connections to our work
Rodin’s system belongs in Foundations because it is a historical and conceptual neighbor, not because every claim must be adopted. It gives us a compact place to compare recurring number patterns, circular mapping, toroidal geometry, and experimental coil work while keeping our own conclusions separate.
3 6 9 →
The site’s broader investigation of recurrence and harmonic structure. Rodin is one contributor to that landscape, not the owner of the numbers.
Flower of Life →
A neighboring visual language of circles, triangular centers, hexagonal order, and 120° relationships. Visual resonance is a prompt for comparison, not evidence of common physical cause.
Unified Field →
The place to compare field interpretations and ask which statements can become equations, measurements, and falsifiable predictions.
Next foundation: lattice and torus
Beryllium’s close-packed crystal, NIST’s triangular arrays of trapped beryllium ions, and helical field lines in tokamaks belong in their own evidence-led thread. They should connect here without being presented as proof of Rodin’s framework.
Questions worth carrying into the laboratory
- Which observed features come from the Rodin path itself, and which come from any distributed toroidal winding?
- How does the field change when wire count, crossing angle, phase, core, and drive frequency change one at a time?
- Can a claimed advantage be expressed before testing as a number with an uncertainty range?
- Does the proposed principle remain meaningful when the same quantities are written in a numeral base other than ten?
- Which diagrams are Rodin’s, which belong to later teachers, and which are modern internet composites?
Source trail and further reading
- Pérez et al., “Portable device for magnetic stimulation: Assessment survival and proliferation in human lymphocytes”Review of Scientific Instruments 84, 094701 (2013). Apparatus, electrical characterization, magnetic-field values, and pilot cell study using a Rodin coil.
- Ramírez-Galindo et al., “Vortex magnetic induction: Mathematical, geometric and experimental characterization”Revista Mexicana de Física 70, 030901 (2024). Biot–Savart treatment, finite-element model, and three-dimensional magnetic-field scan.
- NRICH, University of Cambridge, “Digital Roots”An accessible explanation of repeated digit sums and their equivalence to arithmetic modulo 9.
- Vortex-Based Mathematics community archiveA historical doorway into presentations and community material. It is useful for documenting claims, not as independent scientific validation.
- NIST, “Physicists Benchmark Quantum Simulator with Hundreds of Qubits”A separate real-world connection: beryllium ions forming a nearly perfect triangular lattice in a Penning trap. This is planned for the lattice foundation rather than offered as evidence for Vortex Mathematics.
A useful foundation is a boundary as well as a bridge.
Rodin’s work gives us a memorable map, a buildable object, a large interpretive tradition, and a clear experimental challenge. Preserving all four—without collapsing one into another—lets curiosity stay wide open while evidence keeps its meaning.
