Recursion and Self-Reference

The definition (876)

Note 876 opens with a precise account:

"The concept of recursion is the structure in which a definition contains as a part a reference to this very whole definition. Think of seeing yourself endlessly reflected by a mirror in front and one behind you, as if you were in a tunnel."

Three consequences follow:

The stop condition problem: without a forced halt, recursive structures are endless. "The absence of a stop condition causes values to infinitely self enforce. This Self inflation (or feedback loop) grows out of control and eventually bursts like a bubble."
The exclusion of the outside: "The prerequisite of recursion — the demand for self referentiality — immediately also forbids reference to anything outside of itself."
The identity claim: this exclusion of the outside "reveals the true identity of radical autonomy." Radical autonomy is not freedom as openness to the world — it is self-enclosure, self-definition, the refusal of external reference.

The note concludes with a universalizing move: "everything exists solely through self-definition." Recursion is not just a structural property of certain definitions — it is the condition of all existence.

Forms recursion takes across the practice

Visual / spatial: mise en abyme (878)

Note 878 documents mise en abyme: "Prints of cell phone photo of white cube gallery floor, arranged according to the Laws of Chance, then aligned." The title names the visual structure: an image that contains a smaller version of itself, which contains a smaller version, ad infinitum. The gallery floor photographed within the gallery where it is displayed; the photograph made into prints arranged on that same floor.

The formal recursion is doubled by the process: chance arrangement followed by alignment. Note 856 observes: "The relatively ordered appearance suggests, however, that the artist did not fully relinquish artistic control." Even in a structure aspiring to self-containment through chance, the maker's hand persists. Complete radical autonomy may be an asymptote, not an achieved state.

Documentary: The Work = The Work + Its Documentation (992)

Note 992 states the formula:

The Work = The Work + Its Documentation

The equation is recursive: documentation is constitutive of the work, so the work includes its own documentation, which is part of the work, which includes its own documentation. The record contains what it records; the work contains what accounts for it. There is no outside. This is the documentary form of radical autonomy — the work that needs no external criterion because it carries its criterion within itself.

Circulatory / material: the DeviantArt hand chain (Abrons, 2013)

The press release for Release early, release often… (Abrons Arts Center, 2013) describes recursion as the explicit curatorial premise, and traces it through a specific chain of re-entries:

Hand drawing sourced from DeviantArt
Reappears in a collage
Used as the lead image for About (Wilkinson, London, March 2012)
Reappears in online and print reviews of About
Screenshot of a review printed on a strip of Plexi
Strip twisted into a new spherical Perspex sculpture

This is the physical, temporal enactment of 992's formula: the documentation (exhibition image, reviews, screenshot) re-enters the work as raw material for the next physical iteration. Each release generates context; the context is harvested back. There is no outside — each new step is made from the accumulated record of prior steps (→ openness, release early).

Note 729, which documents the Abrons show, also enacts this: its first related link is back to 729 itself. The note that documents the exhibition about self-reference cites itself as its primary relation.

Titular / linguistic: Senescenence

The exhibition title Senescenence is an intentional misspelling described as "recursive." The word performs what it names. A text on aging has aged in transmission; the error is not a typo but an enactment. The title deteriorates in the act of naming deterioration — a definition that contains a reference to the process it defines (→ Senescenence).

Architectural: Recursive Intervention (2023)

Recursive Intervention: "The exhibition space and the works in it are reflected by a ready-made mirroring inflatable, causing the space to contain a compressed version of itself." The room sees itself; the space contains the space. Recursion made architecturally inhabitable — visitors move inside a structure that includes them within its self-image (→ works-overview).

Cosmological / sacred: the mandala

The Murayama Q&A (2026) — see Mandala Q&A — gives the most direct identification of mandala construction with recursion as a generative principle:

"Mandalas are often recursive structures. Shapes become containers for multiple, smaller shapes, in careful symmetrical subdivision."

The mechanism stated: a context-sensitive Markov chain in which "the distribution of a certain step or operation happening is stochastically determined by the parent the new shape is in." Each new shape inherits a probability distribution conditional on its container, and itself becomes a container for further sub-shapes. The mandala's symmetrical subdivision is not imposed externally but produced bottom-up by parent-conditional stochastic descent through the recursion hierarchy.

This is recursion without the stop-condition pathology of 876: the mandala's symmetrical grammar is itself the stop condition, encoded in the algorithm as a finite recursion depth or a base-case shape. Anicca (2025), Quantizer (2025), and the plotter drawings derived from them (Anobium, Nethermind, Nethermind Quilt) are recursive self-similar structures with built-in halts. They achieve what unbounded recursion cannot: the structure that contains itself without bursting.

The hermetic phrase "as above, so below" — offered in the same Q&A as the answer to how local algorithms reconcile with macro cosmology — is the cosmological version of recursive self-similarity: the same structure obtains at every scale. The mandala, the algorithm, and the cosmos are not separate things to be reconciled; they share a structure.

Iconographic: the Endless Knot — samsara as recursion without halt

Endless Knot (2024) — Sakura fineliner plotter drawing on Hahnemühle watercolour paper, 63×69cm. The work-text is one sentence:

"The endless knot iconography symbolised Samsara i.e., the endless cycle of suffering of birth, death and rebirth within Tibetan Buddhism."

The endless knot — one of the Ashtamangala, the eight auspicious symbols of Tibetan Buddhism — is the iconographic version of what 876 describes structurally. The traditional form is a closed self-intersecting lattice with no terminating point, read as the ceaseless interdependence of cause and effect: saṃsāra, the endless cycle. What 876 calls "Self inflation (or feedback loop)" — the recursive structure that, "[u]nless forcefully brought to a halt, by nature [is] endless" — Tibetan iconography names theologically: a cycle of suffering that turns on itself and cannot be exited from inside.

Two further connections follow.

First, the rendering is the relevant choice — and it is not what the iconography would naively suggest. The traditional symbol is read as one unbroken line; the drawing is not. It is built from a great many short strokes through a hatching algorithm — the same family of translation layers that produces Anobium, Nethermind, and the Senescenence plotter drawings (→ Stained Unravel). A plotter can only draw lines, so the closed-lattice form is reconstituted as density: many parallel and crossing strokes accumulate into the iconographic shape. Occasional pen switches to yellow produce passages that read as oxidized — the symbol of the unending cycle marked, locally, with the visual signature of decay. The structural irony is exact: the icon of saṃsāra — birth, death, rebirth — is fabricated by an algorithm that, in its own operation, has a definite stop condition (the strokes finish; the plot terminates) and that occasionally simulates the aging the icon names. The drawing is not the closed loop; it is the closed loop rendered, by a procedure that halts.

Second, note 976 is an image-only note from 2012 whose Related section pulls it directly into 876's orbit (the only textual link is to the recursion definition itself) — it has no body, only a Facebook-album image and a wikilink chain. The note is itself a "knot" of relations without an explicating sentence: a visual node in the recursion-cluster of the vault. Endless Knot (2024) gives that anonymous image-cluster, twelve years later, an iconographic name and a material instantiation. The earlier note marked the structure without naming it; the later work names what was always already visible in 976's wordless presence.

The work is also structured throughout by 45° angles — both the iconographic lattice and its inscribed lozenge envelope — which places it inside a high-modernist tilted-geometry lineage (Malevich, Mondriaan's tableau-losange, the Mondriaan/Doesburg break, Jan Dibbets), alongside van den Dorpel's own Markov's Window (2004) and Venster (2024) — the latter title being the Dutch word for window, retitling the 2004 work in the artist's mother tongue and selecting the more architectural register (venster, the casement / church-window word) over the domestic raam, so that the recursive frame-as-aperture sense is carried by the noun itself. That lineage and its philosophical stakes — including the lozenge's recursive frame-as-aperture, which is the precise connection back to this page — are developed at length in The Lozenge — Modernist Tilted Geometry.

The Murayama mandala discussion above provides the immediate context: Anicca, Quantizer, and the plotter derivatives (Anobium, Nethermind) are recursive self-similar structures rendered by hatching algorithms with definite halts. The endless knot is their iconographic ancestor: the mandala's symmetrical subdivision and the knot's closed lattice are both inherited forms of recursion-that-contains-itself. The Buddhist tradition built the iconography long before the algorithm; the algorithm now hatches it.

Computational: feedback loops

The artist bio describes "feedback loops" as a design principle. In 709 (artist statement), the feedback loop is described as a condition of complexity: "every single parameter depends on all the others, and my interference amplifies as a feedback loop." A feedback loop is computational recursion: the output feeds back as input, the system at each step includes its own previous state. The system cannot refer outside itself — it operates on its own history (→ subconscious computation).

Systemic: Dissociations as self-training archive

The Dissociations platform trained an algorithm by having the artist eliminate the least coherent element from each trio of notes — the vault we are reading. What the algorithm learned is encoded in the "Related" sections of the notes. The vault is the training data and the output of the trained system. It contains within itself the record of the process that shaped it. This is the institutional form of recursive self-definition (→ protocol, taste, and systems).

The halting problem as the technical version of the stop-condition problem

Note 876 identifies the stop-condition problem: without a forced halt, recursive structures self-inflate and "eventually burst like a bubble." The same problem appears at the level of code: most mutations of computer code produce infinite loops or crashes. This is the halting problem — the provably undecidable question of whether a program will terminate.

Van den Dorpel's solution, in building Mutant Garden, was Cartesian Genetic Programming (CGP): a graph-based representation that constrains mutation to safe computational operations. The graph topology is an internal architectural limit that keeps mutation possible without self-destruction. In other words: creative recursion requires an engineered stop condition. See evolutionary logic for the full account.

Radical autonomy and its costs

Note 876 is careful about what radical autonomy entails. Recursion "forbids reference to anything outside of itself." This is not described approvingly — it is "exclusive and aggressively jealous." The self-inflating system "eventually bursts like a bubble." Radical autonomy is identified as the logical consequence of recursion, not held up as an ideal.

The tension this creates runs through the practice: the system that cannot refer outside itself cannot be accountable to anything outside itself — no external criterion, no external validation, no exit from the loop. But the stop condition problem shows that unchecked recursion destroys itself. The systems in the work typically have built-in thresholds: the cellular automaton reconfigures when it reaches equilibrium; the artist eliminates the least coherent element; the generative organism is allowed to die. These are internal stop conditions — the recursion contains its own limit.

Connection to the semiotic square

The semiotic square maps the logical space of positions (New/Old/Different/Same). Note 876 links directly to 901 (New and Different). The connection: "withdrawing from the endless struggle for the New and the Different" — refusing to be positioned by external cultural criteria — is itself a recursive move. The work that refuses to be located by external reference is enacting the self-enclosure that 876 defines as radical autonomy. The semiotic square names this refusal as "Not New" and "Not Different" — but the note goes further: the refusal of external reference is the structure of all existence.

The phrasing of 901 is precise — "the endless struggle for the New and the Different." That word is not casual. It is the secular translation of Endless Knot's samsara: a cycle of culturally enforced demand that, like Buddhist suffering, cannot be exited from inside — only stepped out of by refusing the position that produces the demand. The same noun ("endless") names both the iconographic-religious and the cultural-aesthetic predicament, and the same operation (withdrawal, profanation, the engineered halt) answers both.