Defensive Publication: Fractal-Modulated Deposition of Interlocking Metal Interfaces

2 Oct 2026

Date and time of disclosure: 2 October 2026, 11:27 British Summer Time (10:27 Coordinated Universal Time)

Declaration

This document is a defensive publication. The inventor places the methods described here in the public domain as prior art from the date of first publication, so that they may not be validly patented by any other party. Every combination of the features described, alone or together, is intended to be disclosed.

Abstract

A method of depositing two or more dissimilar metals so that the boundary between them forms an interlocking, self-similar (fractal) profile that resists delamination. The deposition process, whether electroplating, sputtering, evaporation or similar, is modulated in time and/or space by a control signal derived from a fractal or self-similar mathematical function, such as the Mandelbrot set. Modulation may be applied through electrical current or voltage, or through magnetic fields in one or more planes, at one or more rates simultaneously.

Technical field

Thin-film and electrochemical deposition of metals; multilayer coatings; adhesion and delamination resistance of dissimilar-metal interfaces.

Keywords: fractal interface, electrodeposition, pulse plating, sputtering, vapour deposition, magnetic field modulation, Mandelbrot, multilayer, delamination, interlocking, tungsten.

Problem

Layers of dissimilar metals deposited on each other tend to delaminate. The main causes are:

• differences in thermal expansion and lattice spacing, which build stress at the interface
• weak bonding across a flat, smooth boundary
• a single interface plane, so a crack can run straight along it

A rough interface that interlocks at many size scales would resist crack propagation, because no single flat plane exists for a crack to follow. Existing multilayer deposition methods produce largely flat, regular layers.

Core concept

A deposition process is modulated in time and/or space by a signal derived from a fractal or self-similar function. The modulation varies local growth rate, composition or morphology so that the boundary between two deposited metals forms a self-similar, interlocking profile rather than a flat plane.

Key elements:

1. A fractal-derived control signal (see Signal generation).
2. A deposition process whose growth responds to that signal: electrodeposition, sputtering, evaporation or similar.
3. Alternation between two or more metals, so the fractal profile of one layer is filled and locked by the next.
4. Optionally, the signal is applied at several rates or resolutions at once, so structure forms at several size scales.

The fine-scale structure need not be placed directly. Driving the coarse scales may seed growth instabilities, such as diffusion-limited branching, that carry self-similar structure down to finer scales.

Embodiment A: electroplating

The fractal-derived signal drives the current or voltage between anode and cathode (the article being plated).

• Waveform: the signal sets current density over time. It may be direct current of varying magnitude, pulsed, or alternating with reverse (stripping) intervals.
• Two metals: either a single bath containing salts of both metals, where voltage level selects which metal deposits, or transfer between two baths.
• Growth regimes: high current density gives rough, branching growth; low current density gives smooth fill. The signal switches between the two so each metal grows into and around the other.
• Spatial modulation: an array of segmented anodes, each driven by a different part of the signal, gives a spatial pattern across the surface as well as a time pattern.
• Additional fields: a magnetic field across the bath alters ion flow near the surface through the Lorentz force (magnetohydrodynamic effect). This field may also be fractal-modulated.

Example: tungsten wire with a fractal surface for use as a high-surface-area electrode or emitter.

Embodiment B: vapour and sputter deposition

The fractal-derived signal modulates fields acting on the deposition flux or the growing surface.

• Sputtering: the signal drives the magnetron magnetic field, target power and/or substrate bias. These act on the charged plasma, changing where and how fast material arrives.
• Evaporation: neutral metal vapour is barely affected by magnetic fields, so modulation is applied through evaporation source power, a shutter, ionisation of part of the vapour, or substrate bias and heating.
• Multiple field planes: two or more coil sets, for example X and Y in the substrate plane plus Z normal to it, each driven by the signal at a different rate or resolution. Their combination produces interference patterns with structure at several scales.
• Coil arrays: a grid of individually driven coils, such as printed planar spiral coils, placed behind the substrate gives a spatial field pattern across the surface.
• Alternating metals: two sources or targets alternate under signal control, so each layer grows into the profile of the last.

Signal generation

Any self-similar or fractal function may supply the control signal. Examples:

• Mandelbrot or Julia sets: escape-time values sampled along a line, spiral or path crossing the set boundary, converted to a one-dimensional waveform; or the two-dimensional set mapped directly to a coil or anode array.
• Weierstrass function: continuous, self-similar at every scale, with adjustable roughness.
• 1/f (pink) noise and other power-law spectra.
• Iterated function systems and L-systems.
• Chaotic maps such as the logistic map.

The same signal may be played at several speeds simultaneously, or summed with scaled copies of itself, to target several size scales. The signal may be scaled in amplitude, offset and clipped to stay within the process window.

The Mandelbrot iteration is:

z_{n+1} = z_n^2 + c

Variations, applications and verification

Variations

• Heat treatment after deposition to promote interdiffusion across the interlocked boundary.
• Ultrasonic agitation modulated by the same signal.
• Laser or ion beam exposure patterned by the signal.
• Any pair or series of metals or alloys, including magnetic and non-magnetic combinations.
• Substrates of metal, polymer film, ceramic or glass.

Applications

• Delamination-resistant metal multilayers and coatings.
• High-surface-area electrodes, grids and emitters.
• Heat-radiating surfaces.
• Bonding layers between dissimilar metals.

Verification

• Cross-section the deposit, polish and image by electron microscope.
• Measure interface profile roughness at several magnifications and calculate fractal dimension.
• Compare adhesion against flat-interface controls using scratch, bend or peel tests.

Disclosed aspects

1. A method of depositing a first and second metal in which a control signal derived from a fractal or self-similar function modulates the deposition, producing an interlocking interface between the metals.
2. The method of aspect 1, where the deposition is electrodeposition and the signal controls current or voltage between anode and cathode.
3. The method of aspect 2, where the signal switches between a rough, branching growth regime and a smooth fill regime.
4. The method of aspect 1, where the deposition is sputtering or evaporation and the signal controls magnetic field, source power, substrate bias or shutter timing.
5. The method of any aspect, where magnetic fields in two or more planes are modulated by the signal at different rates to create interference patterns with structure at several scales.
6. The method of any aspect, where an array of separately driven coils or anodes applies the signal as a spatial pattern across the surface.
7. The method of any aspect, where the signal is derived from the Mandelbrot set, a Julia set, the Weierstrass function, 1/f noise, an iterated function system or a chaotic map.
8. The method of any aspect, where the signal is played at several speeds simultaneously or summed with scaled copies of itself.
9. The method of any aspect, followed by heat treatment to promote interdiffusion across the interface.
10. An article made by any aspect, including a coated wire, grid, electrode, emitter or multilayer coating.

Origin and related work

The author first proposed a fractal-surfaced tungsten grid in an earlier blog post. That post's date and link should be added here as supporting evidence.

Related known work, which this disclosure extends:

• US 6663803: fractal interfaces between composite laminates, formed by moulding, to resist delamination.
• Multilayer nickel-tungsten electrodeposition: layers formed by switching current density during plating.
• US 5456690: fractal electrical pulse sequences, applied to defibrillation.

No prior work was found combining a fractal-derived drive signal with metal deposition to form interlocking interfaces. That search was brief and not exhaustive.

Publication record

Item	Detail
First drafted	2 October 2026, 11:27 British Summer Time
Published at	Published at: https://smegot.blogspot.com/2026/10/defensive-publication-fractal-modulated.html
Publication date	2 October 2026, 10:39 Coordinated Universal Time
Independent timestamp