Entfaltung — Unfolding Emma Kunz into Four Dimensions

Entfaltung is German for unfolding — the development of something already implicit into its fuller form. It is the name of a new generative series that begins in research into the pendulum drawings of Emma Kunz, composed in the plane, and ends in a live computation of points in space whose positions change over time. The name describes the method: what Kunz's constructions hold implicitly in two dimensions is unfolded, stage by stage, into three dimensions and then into time.

The series is a forthcoming NFT release. Its alpha is shown for the first time in the Summer 2026 exhibition at Lohaus Gallery — not as a video file but as a live computation, played off a computer through a short-throw projector directly onto the wall. Because every frame is calculated in real time, the piece never repeats. The work currently lives at the unreleased address entfaltung.harm.work.

Genesis, live. The square above is not an image but the piece itself, calculated in real time as you read — drag to pan, scroll to zoom, release to snap. What it shows is the preliminary end point of a process that divides into a research phase and four stages, each with its own body of work and its own relation to Kunz:

Research — study of Kunz's method: the pendulum reading, the radial construction, the systematic sliver-fill.
Stage one (2D) — direct re-drawings of individual Kunz compositions in code: her sheets, reconstructed as programs.
Stage two (2D) — a parametrized generator that generalises her construction into a family of possible drawings, most of which Kunz never drew.
Stage three (2D) — systematic grids that map the generator's parameter space: a cataloguing step with no counterpart in Kunz's practice.
Stage four (3D + time) — the construction raised into space, its points moving over time. This is the departure: from here on the work is no longer a reading of Kunz but van den Dorpel's own.

Behind all four stages sits a private editor in which each drawing is configured; it is documented at the end of the page.

The research — Emma Kunz's method

Emma Kunz (1892–1963) was a Swiss healer, researcher and artist. She made her drawings on graph paper with the aid of a pendulum: she would pose a question, read the pendulum's swings as points and directions, and construct from those readings the radial line-drawings for which she is now known — then fill the resulting cells with colour, sliver by sliver, a fill that reportedly could occupy her for a full uninterrupted working day per sheet. She understood the readings as coming from a higher order and used the drawings as instruments of healing and knowledge; she did not consider them art. Recognition as a twentieth-century abstractionist came decades after her death.

Two features of her method carry directly into Entfaltung:

The drawing is constructed from readings, not composed. In Kunz's own understanding, the pendulum removed her deciding mind from the construction, letting a structure surface that she could not have specified herself. The wiki describes the same posture, reached by algorithmic means, on the subconscious-computation page — the maker as creator and bystander at once.
The form is rule-bound and systematically filled. A grid substrate, radial symmetry, and one local operation — place a sliver, fill a cell — repeated until it accumulates into a global figure. This is the construction logic the sacred-geometry page tracks across the loom, the mandala and stained glass.

Entfaltung begins as research into this method, then asks what remains of it when the pendulum is replaced by a parameter and the page by space. The four stages answer that question in order.

Stage one — re-drawing Kunz in code (2D)

The first body of studies re-draws specific Kunz compositions as two-dimensional generative programs: the radial scaffold, the mirror symmetry and the dense sliver-fill are reconstructed as code rather than transcribed by hand. The relation to Kunz is at its closest here — each study answers to an actual Kunz register — but the fidelity is to the construction, not the surface: the program re-executes how a drawing was made rather than copying what it looks like.

Radial fan. The first emulation, after Kunz's mirrored radial constructions. The symmetry is computed rather than transcribed: the mirror is an operation in the program, not a property traced from the sheet.

Gridded field. The same program tuned to Kunz's tiled register. Where the radial fan works by mirroring, this study works by repetition — one motif restated across a lattice — and it retains the graph-paper substrate that Kunz's own sheets kept visible.

Restrained sheet. Fill density is itself a variable of the program: here it is held low, close to the pencil-on-paper register of Kunz's quieter sheets. The code can under-fill as deliberately as it can saturate.

The bare scaffold. The radial skeleton that underlies many Kunz drawings, drawn without any fill. Separating scaffold from sliver-fill makes the two halves of the method — construction and fill — explicit as distinct steps in the program.

Stage two — generalising the method (2D)

The second body of work stops re-drawing individual sheets and generalises the method: a parametrized generator whose settings span a space of drawings, of which any single Kunz-like sheet is one point. Where stage one asks whether code can reproduce a given drawing, stage two asks what family of drawings the construction can produce. The relation to Kunz shifts accordingly — from her sheets to her procedure. The outputs range from near-monochrome graph-paper studies to saturated black-ground figures.

One point in the family. This output is not derived from any specific Kunz sheet; it is one setting of the generator — a particular point count, fill algorithm and palette — chosen from the space of drawings the construction makes available.

Pushed to saturation. Only one setting differs from the previous figure: the point count. Raising it carries the figure from open to nearly woven, which is what makes the settings legible as axes rather than one-off choices.

The same operation, folded. Some settings produce figures with no counterpart in Kunz's work, like this moiré. The generalisation exceeds the corpus it started from: the generator explores the construction, not the archive.

Toward maximal symmetry. The most symmetric extreme of the range. Stage two's outputs run between the sparse graph-paper studies and figures like this; stage three makes that range systematic.

Stage three — mapping the parameter space (2D)

If stage two opens a parameter space, stage three maps it. Two grids lay the generator out as a matrix, holding every setting constant except two — the generative-art equivalent of a contact sheet, and the same format as the Quantizer trait tables. Kunz has no counterpart to this step: she produced one drawing per question, never a survey of the drawings she did not make.

Scatter grid. Every drawing on the sheet shares all settings except its row and column values, so the sheet reads as one controlled experiment: the effect of each axis is visible by scanning across it.

Asymmetry grid. The second matrix. The grid format treats no single drawing as privileged — what is on display is the generator's range — the same move the practice makes in the N→∞ matrix, the Quantizer catalogue and the fitness landscape.

Stage four — three dimensions, then time

The first three stages stay in Kunz's plane. Stage four leaves it, and this is the move that makes the series van den Dorpel's own work rather than a study of Kunz's: the dimensional count is raised from two to three — points on a plane become points in space — and then a fourth dimension, time, is added, along which the positions of the points change.

Into three dimensions. The same construction logic — points, connecting lines, polygons, sliver-fill — now executed in space. A three-dimensional structure has no single appearance: each viewing angle projects it to a different two-dimensional figure, so rotation alone already yields a sequence of distinct drawings from one object.

How the morph works. The motion is more than rotation. At intervals the system generates a new target configuration for the same set of points, and the points animate from their current positions to the new ones — the morph is a transition between discrete shapes, not an endless drift. Throughout, the number of points and the construction that connects them stay fixed: what changes is the embedding in space — the same vertices and edges, re-positioned. Because the polygons are spanned between the points, moving the points re-shapes every face, and the sliver-fill is recomputed on each re-shaped face. A face that is a thin spike in one configuration opens into a broad facet in the next, and the figure arrives at what reads as an entirely new shape while remaining, structurally, the same object.

The precedent — Manfred Mohr. The nearest precedent in algorithmic art is Manfred Mohr, who from the 1970s onward worked with the n-dimensional hypercube. Mohr's method is exact: the hypercube is a rigid object with a fixed set of vertices and edges; he rotates it in four, five, six or more dimensions and projects the result down to the plane, so all the variety in the image comes from rotation and projection while the object itself never changes. Entfaltung shares the invariant — a fixed set of vertices and connections producing an endless sequence of different figures — but produces the change differently: in Mohr the object is rigid and only its orientation in higher-dimensional space moves; in Entfaltung the points themselves move within three-dimensional space and the object genuinely deforms. The two practices are alike in what stays constant (the structure) and differ in where the change happens (projection of a rigid body versus re-embedding of a flexible one). Where Mohr restricted himself to the monochrome line, Entfaltung carries Kunz's colour and sliver-fill onto the moving faces.

The live computation. The recording documents one run; the exhibited piece is a program, not a playback, and because each frame is computed live no two runs are identical. In the gallery the projection runs autonomously: the rotation cycles through the x, y and z axes and, after a few passes, the structure morphs to a new configuration. The browser version at entfaltung.harm.work is additionally interactive: it can be panned and zoomed, and when released it snaps back to the nearest ninety-degree alignment — the position where the axes of the construction line up and its symmetry, set as a parameter in the editor, becomes visible. From oblique angles the same figure reads as irregular.

The instrument — the editor

The live work is configured in an editor van den Dorpel built for the series: each animated drawing's three-dimensional appearance, points, lines, palette and sliver construction are set there. The editor is not publicly accessible — it may be opened up later, but for now it remains the artist's private instrument, and what ships in the release is its output.

The console. The panel is the concrete form of the parameter space the 2D stages mapped. In the state shown: Drawing is Scatter3D — the stage-one and stage-two generator raised into three dimensions; Points (131) and Seed (452) fix which structure appears, the same point-count axis the scatter grid varied; Symmetry (Octant — all three axes) sets the symmetry the ninety-degree snap later makes visible; Bounding volume and Faces (Volume mesh) build the polygons; Cell colour (By cell face count) and Line colour (By depth) drive the fill and line palettes; Merge coplanar, depth shading (Exponential fog), blend mode (Screen) and saturation set the surface. One console spans the axes the three 2D stages mapped separately, plus the parameters that only exist once the construction has entered space and time.

The pendulum and the parameter

Entfaltung descends from Emma Kunz without adopting her cosmology, and the difference is worth stating exactly. For Kunz, the drawing was received: the pendulum channelled content from outside the maker, and what it received was real — answers about health and cosmos, read from a higher order. In van den Dorpel's practice the drawing is permitted rather than received: the generative system produces content the maker did not specify, but no claim is made that it reports from anywhere ("less composed than initiated"; the apophatic stance the wiki tracks elsewhere).

Stated that way, the two positions share more than they dispute. The pendulum and the parameter are the same device under two cosmologies: both are mechanisms for getting the deciding mind out of the loop so that a structure the maker could not have authored can appear. Note 793 names the want exactly — "find your deepest impulse, and follow that… one trusts what is so discovered, although unclear where it will lead" — and observes the problem: the deepest impulse is not available to direct introspection. Kunz's answer was the pendulum; van den Dorpel's is the generative system. What divides them is not the mechanism but the address of the surplus: Kunz assigns it to a higher order; the practice keeps the apophatic remainder — the relation to what exceeds specification — and drops the positive claim about what is on the other side.

The stages make this legible as a sequence. In stage one Entfaltung is transcription, and the question "received or permitted?" is forced. By stage three the work is no longer any single drawing but a mapped space of them — Kunz drew one channelled answer per question, and the grids draw the space the question lives in. In stage four the metaphysical question dissolves into a structural one, because the object on screen is not a transcript of any one channelling but the whole family of constructions turning.

This is also where the ninety-degree snap carries its meaning. Kunz's drawings are symmetrical because, for her, the higher order was; Entfaltung's symmetry is latent — present in the construction, hidden by viewing angle, recovered by the snap. The work relocates the "higher order" from a metaphysical source to a structural property of the object that the viewer's own movement discloses. The order is real and it is not channelled from anywhere: it was in the rules. That is the sense in which this is van den Dorpel's work and not an homage — the meaning has no location but a vector, the difference between the oblique view and the aligned one, and the viewer's hand traverses it.