Auxetic foams counter-intuitively expand (shrink) under stretching (compression). These foams can exhibit superior mechanical properties such as resistance to shear and indentation, improved toughness and energy absorption (EA) under several types of loadings.
Inspired by the work of Professor Mike Xie and peers at RMIT’s Centre for Innovative Structures and Materials, Nudel has created models of large scale auxetic foam elements, rendered below as large sculptural voxels in the landscape
From one model to the next (using a model)
Nudel has rebuilt our earlier Freeman-Dyson Earth images using Midjourney, an online generative Machine Learning tool available on the Discord platform. Midjourney can take image inputs, combined with new text prompts, to generate new images - using a model to create new models. Generative AI tools have garnered significant public attention since the release of ChatGPT in late 2022 and, more recently, the release of Google Bard in mid 2023. These AI systems are classed as LLM’s (Large Language Models).
A large language model (LLM) is a type of artificial intelligence (AI) algorithm that uses deep learning techniques and massively large data sets to understand, summarize, generate and predict new content. The term generative AI also is closely connected with LLMs, which are, in fact, a type of generative AI that has been specifically architected to help generate text-based content.
Over millennia, humans developed spoken languages to communicate. Language is at the core of all forms of human and technological communications; it provides the words, semantics and grammar needed to convey ideas and concepts. In the AI world, a language model serves a similar purpose, providing a basis to communicate and generate new concepts.
The first AI language models trace their roots to the earliest days of AI. The ELIZA language model debuted in 1966 at MIT and is one of the earliest examples of an AI language model. All language models are first trained on a set of data, and then they make use of various techniques to infer relationships and then generate new content based on the trained data. Language models are commonly used in natural language processing (NLP) applications where a user inputs a query in natural language to generate a result.
An LLM is the evolution of the language model concept in AI that dramatically expands the data used for training and inference. In turn, it provides a massive increase in the capabilities of the AI model. While there isn't a universally accepted figure for how large the data set for training needs to be, an LLM typically has at least one billion or more parameters. Parameters are a machine learning term for the variables present in the model on which it was trained that can be used to infer new content.
https://www.techtarget.com/whatis/definition/large-language-model-LLM
American-English physicist Freeman Dyson speculated on mega-structures encapsulating a star that could harvest all the energy output of its host : the Dyson Sphere
Nudel has speculated at the planetary scale, inspired by terraforming descriptions of otherwise inhospitable planets in Kim Stanley Robinson’s 2312: gigantic sun shading screens covering an entire planet
Based on Uber’s H3 geospatial indexing system, Nudel created a hexagonal mega grid laid across the face of the Earth
TB10_284 2022_11_01 GE - Geodesic_122_R6375_GEOD122_2-002_crop.jpg
TB10_284 2022_09_25 GeoHex Gridded Sphere - Geodesic_122_R6375_01-004_crop.jpg
TB10_284 2022_09_25 GeoHex Gridded Sphere - Geodesic_122_R6375_01-001_crop.jpg
C:\Users\black\Documents\_TB_Google_DRV\_TB_Google_Working_Files\TB10_284 2023 Rhino General\TB10_284 2022_08_27 Geo-Earth Energy Tool\TB10_284 Uber H3 Blog Post Images Nudel\TB10_269 GeoHex Gridded Sphere - Dodecahedron Axes Array_09_crop.jpg
Flat pack of 122 sided Goldberg Polyhedron
Unlike Buckminster Fuller’s Dymaxion mapping (and Uber’s H3 System too), Nudel’s works off a conventionally aligned Icosahedral Goldberg Polyhedron with a pentagon at the poles and one at zero latitude and zero longitude
Nudel has been digesting further the morphology of the brain via a paper in the Journal of Neuroscience: Structural and Functional Analyses of Human Cerebral Cortex Using a Surface-Based Atlas
Nudel’s interest in the neocortex was first piqued by Jeff Hawkins book One Thousand Brains
The Journal of Neuroscience paper describes a basis for determining the surface area of the brain using geometric methods to “unfold” the complex surface of the neocortex to create a map
Human cerebral cortex is a thin sheet of tissue that is extensively convoluted in order for a large surface area to fit within a restricted cranial volume.
The paper also describes several means for mapping the surface of the neocortex
Nudel’s own folded plane model provides a high level abstraction of the brain’s surface that correlates well with the surface area estimate provided in the Journal of Neuroscience paper:
Nudel - 1365 cm3
JoN - 1579 cm3
UK's Globe and Mail website has an article dating back to 2012 on the origins of the phrase "use you noodle". Interestingly, the article also cites the use of "noodle" as a verb for free-form creativity, or to noodle around:
"To noodle around on something, while it does make use of the noodle (head), may derive from the regional German nudeln, to improvise a song, or from the late-19th-century Scottish sense of noodling as humming a song to oneself. By 1937, to noodle was to fool around with notes to create music. By 1942, perhaps by association with the doodle (a loose, free-associating drawing), it acquired the broader sense of messing about with words or ideas without a clear goal."
Nudel has been modelling the human brain, using an ellipsoid set in a tilted plain as a suitable abstraction:
The resulting form has ellipsoid dimensions of 190 x 140 x 150 mm at an angle of 10 degree tilt, giving a resultant volume of 1.8 x 10^6 cubic mm. This brain study is based on the large scale head model made available from the US National Institute for Occupational Safety and Health (NIOSH).
This model also results in a surface area of 75,000 sq mm - comparable to the estimated 150,000 sq mm in the Journal of Neuroscience (Journal of Neuroscience 15 September 1997, 17 (18) 7079-7102; DOI: https://doi.org/10.1523/JNEUROSCI.17-18-07079.1997)
https://www.cdc.gov/niosh/data/datasets/rd-10130-2020-0/default.html
https://www.jneurosci.org/content/17/18/7079
3 arcing Miura surfaces were overlaid on the top of the brain to demonstrate a further abstracting of the folding form of the neocortex surface and show how this folding achieves an efficient packing of surface into the constraints of the skull
Nudel’s post from September 2022 observed the similarities between the surface of the brain’s outer shell, the neocortex, and 3-dimensional folded origami surfaces (such as the Miura fold).
Nudel consulted OpenAI’s ChatGPT to see how an LLM (Large Language Model) might respond to the speculation that the folding form of the neocortex’s surface allows for a large surface area to be accommodated within the confines of the human skull. Here’s what ChatGPT had to say:
The folding of the human neocortex, or the outer layer of the cerebrum, is thought to be an adaptation that has allowed for the expansion of brain surface area within the constraints of the skull. This expansion has allowed for the evolution of increased cognitive abilities such as language, abstract thought, and consciousness.
The folded topology of the neocortex allows for a greater surface area to be packed into a smaller volume, much like how the wrinkles on a brain allow for more gray matter to be packed into the skull. The folds, or gyri, and grooves, or sulci, of the neocortex are thought to have developed as a result of the growth and expansion of the brain during development.
The folding of the neocortex is not unique to humans and is also seen in other primates and some mammals. It is thought that the more highly developed the neocortex is in a species, the more highly folded it will be.
Nudel tested the folding efficiency of a regular Miura fold plane composed of equilateral parrallelograms
Nudel has been experimenting with Goldberg Coexter Construction (GC Construction) of polyhedron face subdivision
The Australian Bureau of Statistics (ABS) provides spatial data covering a wide range of statistical, temporal, and spatial data, including geospatial:
Nudel recently downloaded the Australia - 2021 - Shapefile and imported this into QGIS to convert to a 3-dimensional view of Australia
The shape file was then exported from QGIS as a DXF file and imported into Rhino, with a Lat\Long grid overlaid
A Grasshopper script was used to simplify the outline curve and export the points to a coordinate table in Excel - these curves were then rebuilt in Rhino, representing various levels of abstraction
The abstracted dataset comprising 65 Lat\Long pairs was then reconstructed on the sphere using polar coordinate conversion in Grasshopper
This geodesic outline can then be projected to the plane from the approximate centroid of the Australian continent (at Lat -25 / Long 135) to get a minimally distorted projection
Nudel has been playing with some of the recently released text-to-image AI platforms including
- Midjourney
- Stability
- OpenAI’s DALL-E
One of the best explanations of the recent crop of AI work comes fro
https://podcasts.apple.com/au/podcast/techstuff/id282795787?i=1000580717767
The podcast highlights a real-time application of DeepFake technology in a recent episode of Americas Got Talent with the mapping of judges faces on a trio of performers singing Puccini’s Nessun Dorma
Models are a key focus of Nudel’s research program as they relate to cognition, research, and design.
There are many definitions of the word model. The following definitions refer to a model as a representation of selected aspects of a domain of interest to the modeler:
a physical, mathematical, or otherwise logical representation of a system, entity, phenomenon, or process (DoD 1998);
a representation of one or more concepts that may be realized in the physical world (Friedenthal, Moore, and Steiner 2009);
a simplified representation of a system at some particular point in time or space intended to promote understanding of the real system (Bellinger 2004);
an abstraction of a system, aimed at understanding, communicating, explaining, or designing aspects of interest of that system (Dori 2002); and
a selective representation of some system whose form and content are chosen based on a specific set of concerns; the model is related to the system by an explicit or implicit mapping (Object Management Group 2010).
.Nudel deploys models as a mode of research - a means of exploration/analysis/design through construction.
The images below were constructed in Rhino/Grasshopper as a means to understanding the scale of the brain, in particular the surface area of the neocortex that comprises:
Could this folded topology of the neo-cortex sulci and gyri be modelled as a folded plane, borrowing from a modular origami system, such as Miura-ori
Nudel has been playing with hexagonal sphere divisions, based primarily on Uber’s H3 geospatial indexing system
Uber’s H3 geospatial indexing system
The Uber H3 system relies on a global division that starts with the spherical projection of a 122-sided polyhedron comprising 12 pentagons and 110 hexagons, a type of Goldberg Polyhedron. Uber’s system rotates the sphere so that the pentagons avoid major land areas
Nudel’s mapping deploys the same Goldberg Polyhedron spherical projection conventionally oriented
120 sided polyhedron
Nudel’s interest in Geospatial Indexing is part of a broader research program focussed on models
Earth with conventionally oriented Goldberg Polyhedron
{5+,3}2,2 - TB10_284 2022_09_25 GeoHex Sphere_122_R6375._001
Nudel has been busy on a number of commissioned pieces for private collectors and corporate clients with 2 major installations due for completion in February 2016
The BooleanBoxCross is a prototype of a foyer installation for a boutique hedge fund in Melbourne
Using the Processing language, Mark Nystrom has taken data streams of complex natural phenomenon from a number of sources to produce a series of striking visualizations;
In the search for graphic coding systems, Nüdel came across the work of Dutch Master, Karel Martens. Martens work includes commercial wall fabric designs for Maharam. Based on the deconstruction of a photograph of clouds, taken on the day of his Grandson's birth, Martens reimagines the Pixel;
Listening to a TED lecture by Dan Barasch last week, Nüdel came across this solar canopy proposal for an underground park in New York's Lower East side, with a geometry similar to Nüdel's Galapagos.
The TED lecture can be found at:
Dan Barasch: A park underneath the hustle and bustle of New York City
This is one of Nüdel's favorite scientific discoveries of recent times, the amplituhedron:
http://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/
The amplituhedron is a jewel-like geometric structure that takes particle interaction equations, which can be thousands of terms long, and simplifies them to a single term.
A potentially astonishing consequence of this figure is that a space-time is merely a property of the universe that emerges from the mathematics of geometry.
In our search of a revised identification coding system, Nüdel stumbled upon the work of pioneering algorithmic artist Manfred Mohr recently
http://www.emohr.com/two_1972.html
Mohr produced amongst the earliest computer generated art including a 1973 animation that mines the same territory as Sol LeWitt's Variations of Incomplete Open Cubes
Nüdel is now testing the Mohr/LeWitt degenerate cube figure as a replacement coding system for Nüdel components
