Entfaltung — Unfolding Emma Kunz into Four Dimensions

Entfaltung (German for unfolding) is a series that starts from the pendulum drawings of Emma Kunz. It has two forms, made in parallel from the same programs. The 36 tokens on Ethereum are fully on-chain and computed live: a three-dimensional figure turns, and every fourth block its points move into a new shape. Twenty-five were minted in October 2026 (→ Entfaltung on Chain). The 19 drawings on paper, made between June and October 2026, are drawn by a plotter, and most are then coloured by hand in pencil (→ Entfaltung on Paper). The live work was first shown as an alpha in Summer: Sur Real Real at Lohaus Gallery, Munich (July–September 2026), projected onto the wall with a short-throw projector.

The title is Kunz's word. Her 1953 booklet claims that "the choice of two numbers, connected with each other and unfolded (entfaltet), determines the kind of form and figure", and lists "unfolding (Entfaltung)" among the four factors of form. In the series it names one property of the tokens: each is a single structure, a fixed set of points and connections, that passes through a succession of shapes without a connection ever being cut.

The square above is the Genesis token itself, computed in your browser as you read. Drag to turn it, scroll to zoom, and let go to let it settle.

Kunz's method

Emma Kunz (1892–1963) was a Swiss healer who called herself a researcher (Forscherin). From 1938 she combined working the pendulum, healing and drawing. She wrote little about how a drawing was made. Most of what is known comes from people who watched her, collected with her 1953 booklet in Anna Kipke's 2021 thesis (sources/ingested/kipke-politiken-der-innerlichkeit-2021.md).

A sitting. A drawing answered a question, a patient's or her own. The graph paper lay flat on the table, weighted at the corners. Peter Burri, whom she treated as a boy in 1943, watched her set points with the pendulum, "incredible how fast", until "the whole sheet was strewn with hundreds of points". She then joined a selection of them with ruler and pencil into centres and lines of gravity (Schwerpunkte, Schwerlinien). How she chose which points to join was, to Burri, "a mystery". On these lines she built crosses, circles, stars and parallelograms, and coloured forms, bundles of lines and areas in coloured pencil and oil crayon. The sitting lasted up to 24 hours and ended when she judged the drawing complete. She told Burri she never knew at the start what it would look like.

A second account. Heiny Widmer, who curated her first exhibition in 1973, reports that ordered systems of points "suddenly appeared" in her mind, and that she used the pendulum as a stimulant while building them out: "it seemed as if the picture completed itself outside her consciousness, as if her hands were guided." The two witnesses disagree about where the points came from. Both put the points first and the building-out after.

The answer. The finished drawing was the answer, read afterwards. Kunz worked the pendulum over a small wooden board marked with a cross and interpreted its swing. Finished sheets hung ten to twenty deep on her workroom wall and were taken down again for other cases.

The booklet. In 1953 she published one text under two titles, Das Wunder schöpfender Offenbarung (The Miracle of Creative Revelation) and Neuartige Zeichnungsmethode (A New Drawing Method). Its premise is that every form, circle and parabola included, is made of straight lines, and that two numbers determine a figure. Its first plate, Grundformen (Werk Nr. 019), sets out star polygons inscribed in circles on three, five, seven and nine points, then on six, twelve and eight. With the key published, she wrote, "anyone" could make such figures, "provided he knows how to handle numbers". The fuller explanation she announced at the end never appeared.

Entfaltung takes the construction from this: points on a grid, straight lines between a selection of them, forms on the lines, colour in the slivers where the lines cross. The step no witness could follow, which points to join, is the step the series writes as code. Reconstructing a procedure that its maker called lawful and that nobody else could see is what algorithmic archaeology is for. The series leaves her healing aside. Whether her higher order exists, and where, it keeps as an open question (→ Entfaltung on Paper, Channelling).

Four stages

The work developed in four stages. They are a logical order. On paper, the grid that maps the generator (Tabula I, June 2026) came before most of the radial sheets.

Stage one: Kunz's constructions in code

The first programs re-draw kinds of Kunz sheet: the fan, the tiled field, the circle of chords. They re-execute how a sheet was constructed, so mirror symmetry, point spacing and fill density are settings of the program.

The program re-draws Kunz's Werk Nr. 172 (undated, coloured pencil on paper, ø 68 cm). Lines fan out from one point at the bottom of the circle to the points around the rim, a wedge runs down from the top, and the two lobes appear where the lines crowd. Seraph I, the oldest drawing on paper, comes from the same analysis.

One triangular motif repeated across a lattice, mirrored about a central axis, on the graph-paper ground that Kunz's own sheets leave visible.

A triangle of fans inside a circle of chords, with the fill kept sparse. The four Meridian drawings on paper are built the same way: chords between evenly spaced points on a circle, and fans gathering at points on the vertical axis.

The scaffold without any fill. The program treats construction and fill as separate steps, the same split the drawings on paper make between plotter and hand.

Stage two: a generator

The second stage turns the construction into a generator. Settings such as point count, symmetry, fill algorithm and palette span a family of figures, most of which Kunz never drew. A Kunz-like sheet is one setting among many.

Points on the rim of a many-sided polygon are joined by straight lines, and the slivers where the lines cross are filled as small coloured triangles. The figure comes from no particular Kunz sheet.

The fan from stage one, generated at another setting on a black ground.

Lines run from evenly spaced points on the four edges toward a star at the centre, with bands along the axes and diagonals left empty and a triangle in each corner. The construction is Kunz's Werk Nr. 092 (coloured pencil on graph paper, 110 × 105 cm), the cover image of her 1953 booklet. On paper it became Entfaltung (Emanation) (June 2026).

Stage three: mapping the generator

The third stage lays the generator out as a grid. Each sheet varies two settings and keeps the rest constant, so the effect of each setting can be read across a row or down a column. The format is that of the Quantizer trait tables.

Kunz made surveys too. Grundformen sets out star polygons by point count, an untitled practice tableau first shown in 2021 puts dozens of figures side by side (some dated 1939 and 1962), and three workbooks of constructions survive unpublished. These were her exercises, kept apart from the answer drawings. The Entfaltung grids cross two settings in one matrix, which puts on paper her claim that two numbers determine a form, and they are shown as works.

Across, the number of points. Down, the algorithm that fills the slivers.

Across, the number of outer points (the legs). Down, the offset of the inner points. On paper this grid became Tabula I (June 2026), and Tabula II (September) maps the rule that decides which crossing lines close into a face (→ Entfaltung on Paper, Maps of the program).

Stage four: space and time

In the fourth stage the points leave the plane and become points in space, and then they move. The third dimension was already in a few of Kunz's drawings as projection: some sheets carry three-dimensional coordinate systems with numbers, and a cube on her practice tableau is dated 1939. Points that move were not possible on paper.

The construction is the same in space: points, straight lines between them, faces spanned by the lines, slivers filled. Each viewing angle projects it to a different flat figure, so rotation alone produces a sequence of drawings from one object.

How a token moves. A new Ethereum block arrives about every twelve seconds. In the artist's words, "the Ethereum block hash turns the figure for three blocks and on the fourth moves its points into a new shape, and the program fills the slivers as it renders." Every point is joined to every other, so the points and the connections between them never change; only their positions do. The faces are computed from the positions and rebuilt at every move. Every viewer sees the same figure at the same moment, and nothing is pre-rendered (→ Entfaltung on Chain, How a token moves).

Mohr. The nearest precedent in algorithmic art is Manfred Mohr, who from the 1970s rotated a rigid n-dimensional hypercube and projected it to the plane. In Mohr the object stays rigid and only its orientation changes; in Entfaltung the points move and the object deforms (→ Predecessors of Entfaltung).

Gallery and browser. The recording documents one run, and no two runs are the same. In the gallery the projection runs on its own, turning through its axes and morphing between configurations. In the browser at entfaltung.harm.work the figure can also be panned and zoomed. Released, it snaps to the nearest ninety-degree alignment, where the symmetry set in the editor becomes visible. From oblique angles the same figure looks irregular.

The editor

Each token is configured in a private editor that van den Dorpel built for the series. According to the artist, the editor does not set the composition. In the code, where the points fall comes from the block hash, within the point count, symmetry and bounding fixed for the token; the token's own seed fixes only the reference figure against which each new set of points is matched, so tokens that share those settings move in step. The editor sets what is laid over that structure, namely the complexity of the figure, its shading, its palettes and the method that fills the slivers. These settings are fixed once for each token and become its traits, the same through every reconfiguration. The editor is not public; what is released is its output.

The live structure is on the left and the parameter panel on the right. In the state shown, Drawing is Scatter3D, the stage-two generator in three dimensions. Points is 131 and Seed 452. Symmetry is set on all three axes, the symmetry the ninety-degree snap makes visible. Faces builds a volume mesh, cells are coloured by their number of faces, and lines by depth.

Nesting and the grid. The artist places Entfaltung where two structures in his work meet (November 2026). His earlier generative works were nested: compositions built as hierarchies, parts inside parts. From 2019 he worked with grids, in which each cell is set by its neighbours. In Entfaltung a construction is nested, slivers inside faces inside a figure, and it is repeated: by symmetry across three axes in the tokens, in rows and columns on the Tabula sheets. He attributes the combination to the mathematics that programming with language models opened up to him (→ The Grid, From nesting to the grid).

Agent's reading: the pendulum taken apart

Thesis. The artist's texts name two successors to Kunz's pendulum. The token text says "each block hash is a swing of the pendulum" (→ Entfaltung on Chain). The announcement of the series on harm.work (2026) and the statement on the drawings name the language model the work was developed with: the announcement says "a language model is trained on the collective corpus of human knowledge, and it answers from a source larger than any individual", and the series text calls the drawings "Channeled from a large language model: our collective unconscious" (harm.work; → Entfaltung on Paper, Channelling).

Antithesis. The sources Kipke collects show the pendulum doing three different things. It set coordinates: over the graph paper it located the points. It answered a question: in the sociologist Hubert Knoblauch's history of dowsing, the pendulum is tied to its target only through a question, often unspoken, and its swing is legible only to the person who asked. And it moved only in a hand. Experiments had shown that the dowsing rod moved only in a person's hands, and around 1900 the cause came to be sought in the person, the effect now called ideomotor. The art historian Sara Petrucci calls Kunz's pendulum "an extension of the body". No single instrument in Entfaltung does all three things.

Synthesis: the pendulum taken apart. Each successor is right about one function. The block hash sets coordinates. The language model answers questions. The third function, a hand that keeps moving while the deciding mind does not direct it, is at the pencil, in the stretches the drawings statement describes as "drifting off while my hand continues". The series spreads over three instruments what Kunz kept in one object on a chain. Two things follow. In Kunz's sitting the undirected hand worked at the start, where the points fell; in the drawings it works at the end, in the fill, after code has set the points. And the tokens, which give the fill to the program, keep two of the three functions and lose the hand. Burri reports that late in life Kunz no longer needed the pendulum. If its functions had passed into her hand and her questions, the object could be put down.

See also

• Entfaltung on Paper — the 19 drawings: their constructions and dates; Kunz's method split between tokens and drawings; the channelling question
• Entfaltung on Chain — the 36 tokens: the full graph, the symmetry groups, the 48-second cycle, twin tokens, the traits and every palette
• Predecessors of Entfaltung — Quantizer's block-hash engine, Anicca, Manfred Mohr
• Algorithmic Archaeology — Kunz in the timeline from the loom to the language model; her textile background
• sources/ingested/kipke-politiken-der-innerlichkeit-2021.md — Anna Kipke's 2021 thesis: the eyewitness accounts of a sitting, the orientation board, the 1953 booklet, the history of the pendulum
• Subconscious Computation — the maker as creator and bystander; "find your deepest impulse, and follow that", a line from Bernard Williams's Morality (1972), itself quoting D. H. Lawrence, which 793 recasts in the first person
• Randomness and Pattern — the workmanship of uncertainty in 609, after David Pye's "workmanship of risk"
• Sacred Geometry — rule-based construction across loom, mandala and stained glass
• Quantizer — the trait tables; a live-computed, never-repeating system shown in real time
• Meditative Labour — hand labour beside the generative loop; Kunz called her pendulum sessions "work", and Burri "the hardest labour"