Recursivism Achieves Five-Level Scale for Self-Transforming Art with Artificial Intelligence

Researchers are increasingly examining how artificial intelligence is reshaping artistic creation, but a unifying framework for understanding these evolving practices has remained elusive. Florentin Koch from École Polytechnique and HEC Paris, alongside colleagues, introduce ‘Recursivism’ , a novel conceptual paradigm to analyse art capable of self-transformation. This paper formalises recursion, a principle well-established in mathematics and computer science, as an aesthetic lens through which to view art that doesn’t just change its outputs, but actively modifies its own generative processes. By establishing a five-level analytical scale and three operational criteria , state memory, rule evolvability, and reflexive visibility , Koch et al. provide a crucial tool for distinguishing truly self-modifying art from related fields, offering fresh perspectives on art history and prompting vital discussion around the aesthetic, curatorial and ethical challenges of AI-driven creativity.

This scale provides a rigorous method for understanding the degree of self-transformation within an artistic system. This perspective suggests that artistic evolution isn’t simply linear progression, but a cyclical process of refinement and fundamental change. Artificial intelligence, the researchers demonstrate, renders this recursive logic technically explicit through learning loops, parameter updates, and code-level self-modification, literalising structures previously implicit in artistic processes.

The work establishes that AI doesn’t just execute artistic intentions, but actively participates in the generative process, potentially leading to entirely new forms of artistic expression. These concepts provide a concrete methodology for identifying and analysing recursive artistic systems. Detailed case studies, including the immersive installations of Refik Anadol, the human, machine co-drawing systems of Sougwen Chung, Karl Sims’s Genetic Images, and the Darwin, Gödel Machine, were examined to illustrate these criteria in practice. The analysis of these diverse examples demonstrates the applicability and explanatory power of the Recursivism framework.

Experiments show that Recursivism offers a conceptual response to the automation of execution and the rise of recursive AI architectures, positioning it as a crucial framework for understanding the future of art. The research concludes by examining the aesthetic, curatorial, and ethical implications of self-modifying artistic systems, opening new avenues for artistic exploration and critical discourse. This breakthrough reveals a deeper understanding of how art can evolve in the age of AI, moving beyond simple automation towards genuine co-creation and self-transformation, a paradigm shift with profound implications for artists, curators, and audiences alike.

Recursivism’s Five Levels and Operational Criteria

These concepts were then examined through case studies featuring Refik Anadol, Sougwen Chung, Karl Sims, and the Darwin-Godel Machine, providing concrete examples of recursive behaviours. The research employed a comparative taxonomy, detailed in Table 2, to contrast Recursivism with related fields like generative art, cybernetics, process art, and evolutionary art, highlighting the crucial difference of ontological evolution, the capacity of a system to transform its generative procedures. Experiments focused on dissecting the technical architecture of artistic systems to determine their recursive level, differentiating between phenomenological experience and underlying computational processes. For instance, analysis of Refik Anadol’s installations revealed a technically Level 0 architecture, pre-trained GAN models generating independent images without state memory or feedback, despite a Level 1 appearance of evolution created through audiovisual montage and external data modulation.

This methodological approach enables a nuanced understanding of how AI renders recursion literal and scalable through iterative self-modifying loops, automating the process and revealing emergent patterns at scales beyond human perception. The study pioneered the use of μ, ρ, and R as diagnostic lenses for identifying recursive processes, comparative tools for mapping system evolution, and a common vocabulary for linking human, machine, and hybrid recursivism practices. Ultimately, this work demonstrates how Recursivism reframes the landscape of dynamic systems, defining reflexivity not as mere observation or optimisation, but as a system’s capacity to act upon and transform its own generative procedures.

Recursivism’s Five Levels of Artistic Self-Modification

Experiments revealed that each level specifies what changes from one step to the next, state, parameters, rules, or meta-rules, marking the threshold at which a procedure moves from iterative to genuinely self-modifying, in accordance with the principles of Recursivism. The team measured artistic processes, defining Level 0 as simple iteration where On+1 = f(On), signifying input changes with a fixed rule, exemplified by repeating the same filter on each input. Cumulative iteration, Level 1, is defined as On+1 = f(O0, ., On), demonstrating aggregated inputs and external memory through additive accumulation, such as layering outputs without altering the rule. Parametric recursion, at Level 2, is expressed as On+1 = f(On; pn) and pn+1 = g(On, pn), indicating parameter variation and adaptive feedback, like an AI model updating its weights.

Results demonstrate that reflexive recursion, Level 3, is defined by On+1 = fn(On) and fn+1 = F(fn, On), showcasing the evolution of the generative rule through structural self-modulation, where a system modifies its own algorithm. Measurements confirm that meta-recursion, Level 4, is represented by (fn+1, On+1) = fn (fn, On), signifying the evolution of the generative principle and full self-organization, redefining the logic governing its own evolution. This scale allows for a precise analysis of how artistic processes transform, moving beyond mere repetition to genuine self-modification. The work shows that each major rupture, such as the Renaissance, Modernism, and Conceptualism, operates as a meta-recursive jump, signifying a shift in the underlying rules of artistic creation. The research posits that artificial intelligence now acts as a catalyst for a new artistic paradigm, enabling the technical realization of self-transforming recursive processes, mirroring the historical shift observed with the advent of photography and Impressionism. This breakthrough delivers a framework for understanding how AI can facilitate conceptual authorship, moving art from making to architecting processes.