What if there had been a Chaos/Fractals bubble?

 

Why does one research culture drive a bubble while another does not? COURTESY: Soap Bubbles and Chaos, Journal of Pneumatic Adventures Medium.

 

Modern Artificial Intelligence (AI) research is currently at the heart of a massive financial bubble. It might pop soon, and it might not. "AI" is seemingly everywhere, although its actual value is yet to be determined. I remember learning how to program GPUs in the period around 2010 for applications to computational biology, never thinking that an esoteric research topic could become elemental in propping up the tech economy.

This got me to thinking about what it would look like if we switched out one research area for another, just to highlight any potential absurdities of the situation. So imagine if the field of Chaos and Fractals, quite popular to the point of cliche in the 1980s, was the subject of a financial bubble. It is of note that chaos and fractals were definitely hyped in their time, being featured in movies such as Star Trek: the Wrath of Khan (the Genesis Effect scene) and Ian Malcolm's rhetoric in Jurassic Park. Interestingly, advances in chaos and fractals in particular relied on advances in computing power, initially with supercomputing, and later with GPUs, parallel computing, and quantum computing [1].

In the formative years of chaos, people such as the Eds (Ott and Lorenz) [2, 3] produced a paradigm shift in how complex systems were viewed. The visualization of chaos in the form of fractals were advanced by Benoit Mandelbrot [4]. Fractals were likewise a paradigm shift in how complex phenomena were visualized. In particular, fractals visualize various aspects of chaos using non-Euclidean geometries and relatively simple sets of equations. Their popularity was advanced by a convenient shorthand: visualizations that captured the imagination. While slogans and pretty pictures captured the imagination, the popular imagination got quite far ahead of methodological rigor. This is reminiscent of claims that ascribe properties like sentience or superintelligence to AI systems.

Is this science, or inspiration, or both? Please don't financialize this. COURTESY: Moss and Fog blog.

Eventually, enthusiasm for chaos and fractals regressed back into the fields of physics and mathematics, while also becoming specialized tools for fields like finance. In short, the field matured without the irrational influx of cash, roughly following a Gartner hype cycle. This is curious in light of the limits of AI that people discuss today: regardless of whether or not AI exhibits "true" intelligence, AI systems require intense computational resources to merely be evocative of biological intelligence. But what if there is not a missing component of the intelligence simulation, but of the way in which the underlying system is modeled? Chaos and fractals are not the product of reductionist relationships (as science had been done before), but rather the product of system dynamics, recursivity, and a sensitivity to initial condition. This was the main insight of chaos and fractals, but apparently those insights are not worth a large-scale financial bubble [5].

In their time, fractals were derided as "pretty pictures", and eventually, the pretty pictures could not keep up with methodological trends across the different sciences. But fractals did provide at least one serious insight: systems that look regular at one scale exhibit irregularities apparent at other scales. This has been popularized by the Powers of 10 idea, and further applied to ideas like the coastline paradox. What is particularly interesting to a person who likes complexity approaches to science is that standard hypothesis testing was exposed to many of the same criticisms as chose and fractals. This is despite much more serious consequences of the unaddressed issues with NHST, and has persisted as the scientific norm in spite of superior methods. Quite an interesting exercise in methodological inertia. 

In the current era, AI has partially been driven by advances in methodology, but also by advances in hardware. Central to this has been NVIDIA and their GPU architecture. While GPUs have done much of the heavy lifting in the current AI summer, it is important to remember the origins of GPUs: as a graphical processing tool. This parallels how advances in computing and computational power suddenly opened up our ability to solve and plot the equations of fractal growth and other structures. Perhaps the experience of chaos and fractals will guide AI research after the bubble bursts.

References:

[1] Kaboudian, A., Cherry, E.M., and Fenton, F.H. (2019). Large-scale interactive numerical experiments of chaos, solitons and fractals in real time via GPU in a web browser. Chaos, Solitons & Fractals, 121, 6-29.

[2] Motter, A. and Campbell, D.K. (2013). Chaos at Fifty. Physics Today, 66(5).

[3] Viswanath, D. (2004). The fractal property of the Lorenz attractor. Physica D, 190, 115–128.

[4] Mandelbrot, B.B. and Blumen, A. (1989). Fractal Geometry: What is it, and What Does it do? Royal Society A, 423(1864), 3–16.

[5] Notice that I said "large-scale", which is the distinction between overeager commercialization and financialization. Perhaps financialization is a feature of 21st century popularity, but there does seem to be a difference that makes its way into scientific practice. Fractals are used extensively in attempts to understand the stochastic nature of markets, and have been commercialized in line with that expectation. 

The connections between fractals, efficient markets, and to a lesser extent chaotic behavior is exemplified in books such as:  Peters, E. (1994). Fractal Market Analysis. Wiley.

OpenWorm Annual Meeting 2025 (DevoWorm update)

Here are the slides for the DevoWorm group's report to the OpenWorm Annual Meeting (2024). You can watch Bradly Alicea present the talk on YouTube.

Thanks again to all of our contributors over the past year, all of our Github contributors, and all of our Google Summer of Code applicants. If you are interested in participating, join one of our meetings or contribute to our Github repo and organization.

OA Week: The Troubling U-turn of Open Access

 

Who Owns Our Knowledge? Troubling trends have emerged.

As academics, media producers, and authors: Who Owns Our Knowledge? I present two troubling scenarios. Each of these have happened in the past few decades and is a heady mix of hypocrisy and gross power imbalance.

Intellectual Property Rights!

2006: RIAA Persecutes people for downloading music.

2013: Aaron Schwartz is persecuted for downloading JSTOR articles, resulting in his suicide.

2025: Technology companies use intellectual property without author permissions to train Large Language Models (LLMs). Everyone celebrates tech company profit margins, and LLMs can drive some people to suicide. 

Which of these things is not like the other? To be fair, the final example (in red text) is at the expense of legacy publishers and intellectual property laws. But that is the point. Intellectual property rights are enforced in ways that totally benefit the largest entity. 

Open Access to the.....logical endpoint?

Once upon a time, people were excited about radical open access. Post a preprint, post-peer review, and eliminate the bias of prestige journals. Now, it is the prestigious journals that enjoy Gold (!!) open access (for an exorbitant fee).

Although there are a number of options outside of this paradigm (e.g. Green Open Access), the goals of the open access reform movement seem to have become obscured. More specifically, the transition from words and slogans to institutional normalization has not been smooth.

So is the highlighted scenario the logical endpoint for open access? Probably not, but more work is needed. Not the easy work, but the harder work of changing systems and institutions.

That is all.

Can these scenarios be stopped? This is up to us.

Welcome to our Google Summer of Code scholars for 2025!

 

The Orthogonal Research and Education Laboratory is pleased to welcome three students to the lab as Google Summer of Code (GSoC) scholars. Two (Lalith Baru and Jayadratha Gayen) will be joining the DevoWorm group and one (Vidhi Rohira) will be joining the Open-source Sustainability project.

Lalith and Jayadratha will be working on different aspects of our DevoGraph project (Github). Lalith’s successful project proposal is called “NDP-HNN: Modelling Neural Developmental Programs of C. elegans Using Growing Hypergraph Neural Networks”, while Jayadratha’s successful project proposal is called “DevoTG: Dynamic Graph Neural Networks for Modeling C. elegans Development”. Good luck to both of them! They will be working with the DevoWorm group and active in our weekly meetings. They will also be hosted by the OpenWorm Foundation and contributing to their mission.

Vidhi will be contributing to OREL's Open-source Sustainability project (Github) by working at the intersection of Reinforcement Learning and Agent-based Modeling. Vidhi’s successful project proposal is called “SustainHub: Adaptive Agent-Based Model for Open-Source Community Sustainability”. Check out her updates as part of the Saturday Morning NeuroSim meeting series.

We have also invited our unsuccessful candidates to join our Open-source interest group. We host this meeting every Friday at 12 Noon Eastern time, and cover promoting open-source practices, project development, and project management education.

A review of carcinization: from the biology to computational models

COURTESY: 10 Reasons to Celebrate Darwin Day, Paleontology World, February 14, 2018.

For Darwin Day 2025, I will talk about a form of convergent evolutionary phenomenon called carcinization. Carcinization is the convergent evolution of a crab phenotype. Crablike body plans (defined by a flat, rounded shell and a tail that is folded underneath the body) evolved independently at least five times over the course of Decopod evolution (Hamers, 2023; Wolfe et.al, 2021). This is an example of convergent evolution, where similar phenotypes (and by extension functional evolution) recur in different lineages with ostensibly different underlying molecular mechanisms.

From a phylogenetic perspective, carcinization (acquisition of a crablike body plan) and decarcinization (loss of a crablike body plan) are ubiquitous across marine invertebrates. Ecological selection for such a body type that has led to phenotypic integration of multiple traits, particularly the carapace shape and abdomen (Wolfe et.al, 2021). Figure 1 shows the phylogenetic origins of carcinization in the Brachyura and Anomura clades (infraorders).

Figure 1. A phylogeny showing a variety of crab phenotypes (left), and an illustration of transformation to different crab phenotypes (right). Left image: "How Does a Crustacean Become a Crab", Phys.org. Right image: The "hermit to king" transition within the infraorder Anomura (Tsang et.al, 2011). Click to enlarge.

The most interesting attributes of the carcinization body plan involves: 1) multiple paths to a basic phenotype (shape). Many alternate genotypes result in self-similar phenotype, 2) phenotypic elaboration not due to common ancestry, and 3) a generalized form of common ancestry not at the level of traits. There are varying definitions of carcinization (or brachyurization, see Footnote 1) across genera and orders. The strict definition of McLaughlin and Lemaitre (1997) is a reduction and folding of the abdomen beneath the thorax, or the evolution of a crab-like appearance. 

We can use molecular methods to discover the deep evolutionary relationships between various instances of crab-like phenotypes. Using a mitochondrial phylogeny based on genomic rearrangements of an arthropod protein-coding gene, Morrison et.al (2002) suggest that once they appear, the independent evolution of crab-like forms may be irreversible. Another study by Wolfe et.al (2019) utilize nuclear genes and the Anchored Hybrid Enrichment (AHE) method to confirm monophyletic (single origin) relationships between all infraorders of the clade Decopoda. They also demonstrate that monophyletic "lobster" and "crab" groups exist. In terms of developmental origins, carcinization involves Brachyury (T-box Genes): great detail for its pivotal role in the development of the notochord and posterior mesoderm (Papaioannou, 2014; see also Footnote 1). Carcinization results from several transcriptional mechanisms related to physiology and phenotype, including energy metabolism-related pathways, ventral nerve cord fusion and associated apoptosis, metamorphosis, and abdominal-specific Hox genes (Yang et.al, 2021).

The evolution and development of the crab-like body plan can be characterized computationally in order to expand our understanding of convergent evolution in the evolution of development. There are a number of means to build a computational model of this process. Ostachuk (2021) proposes a network-based topological model of crab metamorphic development. In this model, the stages of brachyuran metamorphosis are modeled as a series of complex networks. Figure 2 shows this process of defining morphological unit centroids as network nodes, and topological transformations between morphological units as the network edges. A topological overlap analysis was conducted to demonstrate changes in phenotypic complexity. Traditional measures of complexity, such as modularity and hierarchical organization, increase across the course of development. This corresponds to what Ostachuk (2021) defines as a transition from intensive to extensive complexity.

Figure 2. A network of morphological units derived from a crab-like phenotype. From Figure 1B, Ostachuk, 2021. Click to enlarge.

Figure 3. A comparison of developmental network topologies from egg to crab phenotype. From Figure 3 in Ostachuk, 2021. Click to enlarge.

Ostachuk (2021) uses morphological networks rather than gene regulatory networks (GRNs) because it is difficult to make a mapping from network outputs to topological transformations of the phenotype. Yet one benefit of using genomic representations is to allow for a further representation of canalized morphogenesis. This is consistent with Waddington's notion of reduced sensitivity to genetic or environmental perturbations (Agam and Braun, 2025) and is amenable to understanding via an epigenetic landscape model. The epigenetic landscape model (Wang et.al, 2011) in particular is useful for modeling the evo-devo of carcinization. According to our evolutionary examples, we should expect the landscape to converge during development. A prediction can be made that most stable points in the epigenetic landscape favor a path towards crab-like phenotypes. Molecular mechanisms such as Hsp90 can provide a mechanism for phenotypic divergence in cavefish. Yet phenotypic buffering mechanisms can also work the other direction: multiple configurations of genomic loci converge to the same phenotype (Kovuri et.al, 2023). This phenotype tends to become irreversible as other options are no longer developmentally viable. Indeed, evolutionary irreversibility can be represented as a saddle node, a pitchfork bifurcation where two developmental pathways diverge (Ferrell, 2012).

Carcinization can also be summarized in the form of a computational genotype-phenotype map (Figure 4). On such a map, we can approximate convergent evolution as multiple genotypic representations that converge to a single phenotype. Genotype-phenotype maps also allow convergent evolution to be viewed as a study in self-similarity. In the complexity literature, self-similarity is defined as a complex system with the same statistical properties at multiple powers of magnitude (Magnusson, 2023). Figure 4 demonstrates three different types of genotype-phenotype maps: GRNs to phenotypic modules (Figure 4A), a correspondence map that maps between domains (Figure 4B), and a genotypic representation that maps to a phenotypic representation (Figure 4C). In Figure 4A, the output of three GRNs (G1, G2, G3) are mapped to four phenotypic modules (P1, P2, P3, P4). Each GRN can map their outputs to multiple phenotypic modules, components of a phenotype that we observe in the crab-like body plan. This allows us to estimate the contribution of each GRN to each phenotypic module (Wagner et.al, 2007; see also Footnote 2). Figure 4B provides a means to understand the space of genotypic variation and how this corresponds to the space of all possible phenotypic configurations. While the example we give is not specific to crab-like body plans, in such a case a wide variety of GRN activities (W_g) will correspond to a constrained set of locations in the phenotypic map (W_p). This allows us to apply more sophisticated Computational Biology models such as joint manifolds (Munteanu and Sole, 2008). To conclude, Figure 4C demonstrates the concept of phenotypic redundancy (Ahnert, 2017), which is a common feature of phenotypic maps. Phenotypic redundancy can also help us understand how multiple genotypic representations can converge upon a self-similar phenotype. Our genotypic representation contains a simple chromosome with multiple loci, which in Figure 4C are recombined and mutated across our three examples. Our phenotype is a 2-D layer of black and white cells, which result from the expression of the genotypic representation. Based on an application of theory, the crab-like body plan can be said to exhibit robustness against gene duplication, mutation, and recombination events.

Figure 4. Genotype-Phenotype map components. A) discrete model of genomic elements (containing a GRN) with their outputs mapping to different phenotypic modules, B) correspondence map showing how genotypic elements in domain W_g map to phenotypic elements in domain W_p, C) genotypic representations that converge upon a single phenotypic representation. Click to enlarge.

Let us conclude with two items for further study. Wolfe et.al (2021) asks: can you predict a phenotype from ecology or genomics? In the case of carcinization, we observe repeated gain and loss of body plan: polyphyletic nature of crab phenotype. We might also be able to predict crab-like phenotypes from the results of computational models. The developmental network and epigenetic landscape approaches are particularly promising in this regard. Might carcinization be a form of developmental buffering as predicted by the epigenetic landscape model? Patterson and Klingenberg (2007) suggest that phenotypic buffering is triggered by Hsp90 activities in flies, fish, and plants. Genotype-phenotype maps are indeed possible but require a complete characterization of the genetic diversity underlying the multitude examples of crab-like phenotypes found in nature.

Footnotes:

1. Brachyurization is perhaps related to brachyury, which involves with the epithelial-mesenchymal transition in development. A description of this process is reviewed in Huang et.al (2022) and Haerinck et.al (2023).

2. Further discussion of conducting genotype-phenotype mapping using network approaches are presented in Kim and Przytycka (2013).

References:

Agam, O. and Braun, E. (2025). Stochastic morphological swings in Hydra regeneration: a manifestation of noisy canalized morphogenesis. PNAS, 122, e2415736121. 

Ahnert, S.E. (2017). Structural properties of genotype–phenotype maps. Royal Society Interface, 14(132), 20170275.

Ferrell, J.E. (2012). Bistability, Bifurcations, and Waddington's Epigenetic Landscape. Current Biology, 22(11), R458-R466.

Haerinck, J., Goossens, S., and Berx, G. (2023). The epithelial–mesenchymal plasticity landscape: principles of design and mechanisms of regulation. Nature Reviews Genetics, 24, 590–609.

Hamers, L. (2023). Why do animals keep evolving into crabs? LiveScience, June 1.

Huang, Z., Zhang, Z., Zhou, C., Liu, L., and Huang, C. (2022). Epithelial–mesenchymal transition: The history, regulatory mechanism, and cancer therapeutic opportunities. MedComm, 3(2), e144. doi:10. 1002/mco2.144.

Khodaee, F., Zandie, R., and Edelman, E.R. (2025). Multimodal learning for mapping genotype–phenotype dynamics. Nature Computational Science, doi:10.1038/s43588-024-00765-7.

Kim, Y-A. and Przytycka, T.M. (2013). Bridging the Gap between Genotype and Phenotype via Network Approaches. Frontiers in Genetics, 3, 227.

Kovuri, P., Yadav, A., and Sinha, H. (2023). Role of genetic architecture in phenotypic plasticity. Trends in Genetics, 39, 703-714.

Magnusson, M.S. (2023). Sudden bio-mathematical self-similarity and the uniqueness of human mass societies: from T-patterns and T-strings to T-societies. Frontiers in Psychology, 14, 1157315. 

McLaughlin, P.A. and Lemaitre, R. (1997). Carcinization in the Anomura: fact or fiction? I. Evidence from adult morphology. Contributions to Zoology, 67(2), 79-123.

Morrison, C.L., Harvey, A.W., Lavery, S., Tieu, K., Huang, Y., and Cunningham, C.W. (2002). Mitochondrial Gene Rearrangements Confirm the Parallel Evolution of the Crab-like Form. Royal Society B, 269(1489), 345-350.

Munteanu, A. and Sole, R. (2008). Neutrality and Robustness in Evo-Devo: Emergence of Lateral Inhibition. PLoS Computational Biology, 4(11), e1000226. 

Ostachuk, A. (2021). A network analysis of crab metamorphosis and the hypothesis of development as a process of unfolding of an intensive complexity. Scientific Reports, 11, 9551.

Papaioannou, V.E. (2014). The T-box gene family: emerging roles in development, stem cells and cancer. Development, 141(20), 3819–3833.

Patterson, J.S. and Klingenberg, C.P. (2007). Developmental buffering: how many genes? Evolution and Development, 9(6), 525–526.

Tsang, L-M., Chan, T-Y., Ahyong, S., and Chu, K-H. (2011). Hermit to King, or Hermit to All: Multiple Transitions to Crab-like Forms from Hermit Crab Ancestors. Systematic Biology, 60(5), 616-629.

Wagner, G.P., Pavlicev, M., and Cheverud, J.M. (2007). The road to modularity. Nature Reviews Genetics, 8, 921–931.

Wang, J., Zhang, K., Xu, L., and Wang, E. (2011). Quantifying the Waddington landscape and biological paths for development and differentiation. PNAS, 108(20), 8257–8262. 

Wolfe, J.M., Breinholt, J.W., Crandall, K.A., Lemmon, A.R., Moriarty Lemmon, E., Timm, L.E., Siddall, M.E., and Bracken-Grissom, H. (2019). A phylogenomic framework, evolutionary timeline and genomic resources for comparative studies of decapod crustaceans. Proceedings in Biological Science, 286(1901), 20190079.

Wolfe, J.M., Luque, J., and Bracken-Grissom, H.D. (2021). How to become a crab: Phenotypic constraints on a recurring body plan. BioEssays, 2100020.

Yang, Y., Cui, Z., Feng, T., Bao, C., and Xu, Y. (2021). Transcriptome analysis elucidates key changes of pleon in the process of carcinization. Journal of Oceanology and Limnology, 39, 1471–1484.