This week, I experimented a bit and looked into how to refine a 3D structure in the spirit of "jitterbugs" (see earlier posts), containing correlations of node spins similar to those we might find in nature. I wanted to produce the sorts of rotations present in the model I built from straws (see Week 2 video). It seemed that the 3D-printed models I was using did not enable enough freedom for the blue tetrahedra to wiggle around in addition to turn, so I loosened them a bit. But finally, as I was exploring how to do this, I realized that actually, the sorts of rotation in the straws video were rather different from the sorts of modes of rotation expected in nature. The key effect I wanted to capture was that galaxies joined by "filaments" tended to have similar rotations, but this model may deform the filament too much. It would be great if we could explicitly add rotating rods joined by some sort of hinges of nodes in a network ... These sorts of rotating rods in a network might have some interesting mathematical properties. The sense of rotation (clockwise or counterclockwise) gets preserved through the network like water flowing through the straws that I made my initial model out of, and certain combinations of clockwise and counterclockwise would turn out to be impossible. In any case, this rotating-rod model might be too much for the project with Lizzy, since I myself have trouble fully grasping its properties ... While I continue to think about how to make something along those lines work, I will get more heavily involved with helping Lizzy to wrangle the data from my simulations. The video is a new one I made for my research, similar to one from last week, but with more compact nodes (thus, they are less likely to form filaments folds between them). The left-hand panel is a "crease pattern" for folding up the structures whose densities are shown at right. The blue regions end up face-up in the folded image, while the red regions end up face-down. The curves between the two colors are where the sheet would get folded. Don't try folding this at home though! In fact, to accurately fold the patterns at right, you would need an extra spatial dimension, since a 2-dimensional dark-matter sheet folds up in 4 dimensional phase space (with the added 2 dimensions of velocity.) I have also changed the color scale so that the highest-density pixels in the right panels turn yellow, suggestive of star formation. That is what happens in nature, roughly -- only the highest-density places in the universe are where stars form. Surprisingly, some of these highest-density points are along the edges of the structure -- this could be a way to test whether dark matter truly does nothing special when it collides with other patches of dark matter, as assumed for this simulation. This "collisionlessness" is the only way it is possible to get several layers of the sheet to overlap, with different velocities, in the same location. Another interesting thing about this video is that the "Cairo pentagonal tessellation pattern" (see https://en.wikipedia.org/wiki/Cairo_pentagonal_tiling) extends even into the inner structures of the blobs. Usually, the dynamics inside collapsed structures like this are thought to be too complicated to understand, but the persistence of this pattern inside the blob raises some hope that we can understand the formation of that structure. More philosophically, it may indicate a way that the arrangement of blobs around a galaxy (like Andromeda around our Milky Way) influences the structure inside our Galaxy. To see how the tessellation pattern influences the pattern, look at the below figure, a frame from a similar video when only one blob is on its own, without any influence from neighbors. All the boundaries are entirely circular, not the polygons we see when blobs form with external influence. Anyway, until next week! -Mark Lizzy's update
I have been thinking about the simulation data Mark has sent in the form of some position-velocity phase portraits, video, and snapshots. I’ll be assembling everything into a blog that I can access like a virtual sketchbook! I’m really interested in getting visually acquainted with the imagery, talking with Mark about how it fits into his work, and musing with him on sharing this side of scientists’ work. Dark matter is a colossal topic. Cosmology research scratches the itch of our wondering how the universe exists the way it does. The research implies that patterns pervade not only large scale structures, but are preserved inside dense areas as well. The most counter-intuitive element to all of this that I’ve come across is that the “sheet of paper” stretches in void areas and bunches up in dense areas. Neither a paper model, nor the 3D model we’re brainstorming solve that visualization problem. This concept carries over to 3D space as well, which means the dark matter sheet (remember, three-dimensional), twisting and folding into dense pockets, attracts ordinary matter into the densest regions, while the void space in between stretches, further pushing the dark matter sheet, and ordinary matter, into denser and denser folded patterns. I used to think galaxies formed because of black holes. I honestly had no idea dark matter played the type of role it does according to Mark’s research! Something that tipped scientists off to dark matter’s significance was the discrepancy between calculated mass of galaxies according to their black hole activity vs. observed mass. There was far more mass recorded than calculated, which meant something else must be attracting and aggregating matter. Enter: Dark Matter, so called because it is as-of-yet unobservable except by its effects. This anecdote is just one of many that illustrates the importance of the scientific method, testing hypotheses with designed experiments, and analyzing the results for what you perhaps weren’t expecting to see. Without the ability to abstract observations into some quantitative data, some meaningful findings, and do so concisely, there would be no science! Not only is that abstraction interesting to me cognitively, the subsequent imperative to represent that abstraction in order to communicate it efficiently has probably evolutionarily shaped our entire systems of communication and representation. Plotting is one of those abstract communication tools that is just conceptually so rich to me. This is why I’d like to look at Mark’s data, plots, and graphs and make some art out of and about them. I'm planning out some projects now, and will let you know next week when I can expect to have some work to share!
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Lizzy's update Short update this week! Mark sent along data and visualizations that will act as raw materials for some series of multi-media art. Here is an example of what he sent in visual form: I just want to peel back those layers and see what’s in there! The x-axis shows position as a number line, and the y-axis shows velocity. Here is an instructive diagram of a phase portrait from a quick image search: (For example, an idealized pendulum that swings evenly without dampening. Negative velocity is a counter-intuitive thing, but it just means velocity in the opposite direction of whatever is defined as the positive direction.) The data that Mark sent is just the thing I was looking for, so I will be getting more info from him in our next video chat about what exactly we are looking at, since the graphs are not labeled, and I’m still a bit unfamiliar with the data! It is likely that I will download a free visualization program called ParaView that Mark used for the above images. My partner and fiance Craig Hamel, a G.R.A. at Georgia Tech, is graciously teaching me aspects of Python so I can more easily navigate the data. In the past, I have taken image “slices” from data sets, for example, just one of the colored lines in the graphs above, and projected them onto surfaces to be traced as either a standalone 2D image or a slice of a 3D object to be cut out and assembled. I will use with the same technique, which draws a connecting line for the viewer to enter the world of STEM through familiar materials such as charcoal on paper or cut plywood, something “analogue” vs. digital. I will also work in the medium of printmaking, which has its own material implications of the recording, copying, and passage of information, that can add layers of meaning to works about and comprised of data describing the early universe. Mark and I are still working out our tetrahedral collapse toy model! Here is a sketch I made in anticipation of creating multiple pieces to connect together: In theory, twisting one blue tetrahedron would cause all other blue tetrahedra to rotate in correlation. I have postponed my update on “Order in Space” until next time, but I will leave you with this quote: “The growth in understanding of spatial order seems to follow closely man’s own evolution as a conscious being. First as a tool of orientation, the ‘where’ of things, and eventually becoming the ‘how’ inherent in things.” (Critchlow, 3) Critchlow, Keith. Order in Space: A Design Source Book. London: Thames & Hudson, 1969. Mark's update I have a few cool things to report: 1. An article I wrote is now published, in the current issue #122 of the origami magazine The Paper. (see below). There's a lot of stuff in those two pages, and fellow SciArt Resident Ben Andrew happened to have taken the picture there! 2. I've updated a simulation shown in Fig. 2 of that article, and made the following video (see below). This shows a "pentagonal Cairo tessellation" of voids, with galaxies residing at each vertex. As time passes in the video, the galaxies form, together with filaments between them. The left panel shows the “crease pattern,” showing matter at its initial location on the cosmological sheet, before folding up. If the sheet were placed on a table and folded like paper origami, blue regions would end up face-up, and red regions face-down. Borders between red and blue regions are the creases. The right panels show the “folded form,” rendered as though backlit. In light regions, the sheet has stretched out, allowing a lot of light through. Dark regions are high-density (with a lot of the sheet in a small area), with multiple layers overlapping." The rightmost panels are close-ups of the three-filament and four-filament galaxies. 3. I have a rough prototype of a "tetrahedral void" model that I've discussed in previous blog posts, made from 3D-printed pieces (see below). I'm using rubber bands to attaching the "galaxies" to each other, holding them to onto the central void tetrahedron (giving it "tensegrity", a word Lizzy taught me -- I hope I'm using it right!). The main point of this model was that neighboring galaxies would tend to spin together on it, but this doesn't happen particularly impressively, for a few reasons, such as too-tight rubber bands, and that alternative attachment arrangements would better encourage this behavior (requiring different-sized rubber bands, unfortunately). It may not work as originally conceived, but it is still helping me figure out how the predictions of the model should work! And I think a nice piece of tactile art should be able to come out of it. 4. Lizzy mentioned the book Order in Space by Kieth Critchlow; this happened to feature a concentric-tetrahedron shape similar to my "tetrahedral void" model. Looking that book up, I saw another book by him, Islamic Patterns: an analytical and cosmological approach. The word "cosmological" definitely drew my eye! Luckily, my university library does carry the book, and I checked it out. Although here "cosmological" refers to a spiritual worldview -- there are many numerological aspects of Platonic solids and planar tessellations as they are applied in Islamic art that I had no idea about! Honestly, there seems to be little to no relationship of these patterns to the modern science of cosmology, though ... the book features some patterns in a similar vein as the "Cairo pentagonal tessellation" underlying the arrangement of voids in the video in this post, but this arrangement is very idealized; we would not expect this exact kind of pattern to arise in nature! But the inner structure of the forming galaxies is nonetheless much more regular than many cosmologists assume it is, which probably carries over to some degree in reality.
That's all for this week ... Lizzy's update Although I was traveling over the last weekend, Mark and I met via video chat and asked and answered some questions. I was interested to hear about the “Celebrate Science” event at University of Durham. It turns out, the event was attended by mostly children, who typically have a hard time folding the origami tessellations related to Mark’s work. Maybe this is something we can work on! Model kits and model making from paper, in my experience, require a well designed instructional booklet. There was mention of virus geometry being a topic at the event, and I told Mark that there is a huge crossover between mathematics and geometry, and cell or molecular structure. For example, most virus shells, or capsids, are formed in either a helical-cylindrical shape, or an icosahedral-spherical shape. The mention led me to one of my favorite resources, “Order in Space: A Design Source Book” by Keith Critchlow. I will share a bit more on that next week… it’s gonna get philosophical. In my travels last week, I reconnected with a colleague from my former art studio in Newark, NJ, artist and master papermaker at Rutgers University, Anne Q. McKeown, who just so happened to attend Julia Buntaine’s talk on neuroaesthetics, something I have not studied for some years! Anne and I both find the subject captivating. Dusting off those bookshelves in my memory, I recall writing in my sketchbooks about the process that happens in the mind when one looks at, well, anything! Scribbled notes on the TEDtalks of Dr. Ramachandran... pages from the sketchbooks of Ramon y Cajal… I still think about what must happen, neurologically, when looking off into a distant landscape… And I am brought back to much of the jargon-y vocabulary that lets me communicate these concepts with the STEM community, whereas in my art studio, I tend to use much different words. For example, bottom-up and top-down thinking came back into my consciousness this week through a PRI broadcast and article featuring neuroscientist Dr. Eric Kandel, and I briefly explained the concept to Mark. I frame my artworks in this context, offering something familiar for the visual system to chew on, utilizing bottom-up thinking, taking into account all that we already know, and then accenting or augmenting it with some information that requires top-down thinking, something that demands personal context, imagination, and interpretation. The top-down approach, as is mentioned in the insightful interview linked above, allows the viewer to engage in a creative process of their own while viewing an abstract artwork, something that sets modern and abstract art apart from its figurative counterpart. Mark said it’s taken him some practice when reading papers to engage his top-down thinking, to ensure that he’s not getting bogged down in the nitty-gritty details of analysis, and so he can come away from a paper with an idea of how it fits into the greater context of his own contribution and expertise. Instead of a rote exercise, it becomes a fulfilling creative process. After some thoughts on the viewer, then comes of the question of content. One of the greatest privileges of being partnered with a scientist is being able to pick his brain on questions I wouldn’t be able to ask anyone else! For example, if I am an artist making art using scientific data, I, as an artist, may be attracted to some portion of data that seems interesting from my perspective, but how does that fit into what the scientists deem to be interesting or important? We’ll be keeping this in mind as Mark collects some data for me to manipulate into different visualizations and graphs. What will happen when artworks contain familiarities like the coordinate system, labels and keys normally found in graphs, or simply the impression of data through the use of color and line, the types of visual imagery we as 21st century folks are more and more exposed to everyday through our interactions with technology? What can be added, altered, or omitted so that the work demands the viewer to imagine and subjectively interpret what is in front of them? It’s that personal connection to science (technology, engineering, math…) through art, that I aim to evoke in the viewer. How will our work on visualizations of the origami tessellation of the dark-matter sheet create opportunities for learning and insight, as well as creative engagement from the viewer? We may have to come up with a hypothesis. Mark's update In a previous couple of blog entries, I discussed a model, inspired by some "jitterbug" models that Lizzy shared with me, that shows how neighboring galaxies tend to spin in the same direction. The design makes this model tactile: turning one tetrahedron will turn all its neighbors at the same time (as may be seen in a previous blog video, in which I rotated tetrahedral elements of a model built from straws). I tried 3D-printing a somewhat more sophisticated version of this design. That succeeded as I designed it: I designed the small blue tetrahedra to be able to spin and move completely freely around ball joints connected to the white, large tetrahedron. I planned to hold the 4 pieces of this model together by attaching them with rubber bands, but unfortunately, I could not manage to do that! It was not even clear to me that the design would hold together stably if I were to manage it. So, I will change the design, to allow the tetrahedra not to move arbitrarily around the ball, but to just rotate around pegs ... this should capture the relevant motions.
In a meeting last week, Lizzy and I also discussed the fascinating structure and substructure of a galaxy in so-called phase space, and in the next couple of days I will providing her with some data that she can play with. Happy Halloween! Lizzy's update Mark’s interest in creating a dynamic 3D object based on the tetrahedral collapse model of early structure formation in the universe has lead to a design challenge: what kind of hinge or connection would be mechanically practical, and how does that physical mechanism relate to the concept of changes in density of the dark-matter sheet? Mark has designed a first draft of a ball joint connection that he’ll be able to 3D print at Durham University. The advantage of rapid prototyping and manufacturing these objects would be to create an expansive three dimensional matrix of twisting polyhedra. It can serve to demonstrate three dimensional folding of space as well as offer a point of entry for viewers to immerse themselves in a physical, albeit abstract, model of the early universe. We will share our progress on this as we make it! On that note, I’m hitting the brakes! Back up. There is so much for me to dig into in just the first paragraphs of just ONE of Mark’s papers. I’ll be creating series from points of inspirations like the following. Here in front of me is “Tessellating the cosmological dark-matter sheet: origami creases in the universe and ways to find them” An excerpt reads “As particles move around in three-dimensional space, they occupy worldlines in four-dimensional space-time.” I can only think of Billy and the Tralfamadorians from Kurt Vonnegut’s Slaughterhouse Five. I imagine each and every particle from the dawn of creation existing as an eternal smear through space-time, neither becoming or ceasing to exist, a meaningful visualization for contemplating quantum entanglement. The Tralfamadorians are aliens that exist outside of time and perceive time-based creatures, and the universe itself, as sort of a film strip, with moments stacked one on top of another continuously, accessible as a whole or one moment "at a time"... The paper continues, “It is also useful to think of particle trajectories in yet another, six-dimensional ‘phase space’ of position and velocity. Each particle in the universe can be plotted in this 6D phase space, three of the dimensions given by its spatial position [x, y and z axis from an origin], and three by its velocity [a vector quantity, vectors requiring a magnitude and direction to define them].” What would a 6-dimension-perceiving Vonnegut alien see? We will never know. In fact, attempting to visualize dimensions higher than three or four is often counterproductive. After all, mathematics is conceptual, abstract, and removed from the physical reality on which we we base our concept of sight and materiality. So I have taken to presenting direct translations of mathematical graphs as art for contemplation, similar to the way an artist might present an idyllic landscape or portrait. There is an inherent beauty that I see, maybe its that I conceptualize it more than see it, in systems, graphs, and plots, like the phase portrait below. What happens when a new system of presenting information is introduced into art-making? All artists do it, and I think the systems we create make up a large part of our style and vision. Some distill an essential quality from observing the natural world and create a visual language that way. Some borrow from art history and each other, some from technologies like microscopes or telescopes, extensions of the visual system, some from abstract emotional systems. I am interested in what happens when the mathematical and scientific systems are used to create art. Works that still reflect some essential quality of the natural world, or make visible an otherwise invisible connection. I’ll be collecting some data from Mark to use as sort of a still-life of information to “draw from,” to create works that weave art and science, with an appreciation for mathematics, graphs, and plots. Mark's update I have been thinking about and have started to design 3D-printed pieces to represent galaxy spins; my department does have a 3D printer that I could use for that purpose. The idea got its root from "jitterbugs," mentioned in previous blog entries. Lizzy and I are trying to think of how to make something that either seems to fold naturally, as jitterbugs seem to, or that illustrate how spins of galaxies in a network affect each other. The simplest such 3D network would be a set of galaxies arranged in a tetrahedron; it appears below, with a ball joint at each vertex to attach a galaxy. The galaxies would attach to each ball, and look something like this (scale blown up; the inside of the sphere below is the same size as the balls on each vertex above): This week, also I am helping out at a "Celebrate Science" event here in Durham, UK, where I will bring some origami designs; I call the activity "fold your own galaxy". That's about all for now; hopefully next week I'll be able to report on the 3D printing ... it will probably require some tweaking.
Mark's update One idea we're exploring is to make an object like the prototype in the below movie. It's related to how the direction of one galaxy's spin direction might get associated with another galaxy's spin direction, if it's connected on the "cosmic web" network that links together galaxies in the universe. This represents galaxies around a cosmic void (the tetrahedron in the center), with other tetrahedra (that represent galaxies) attached to each vertex. Each tetrahedron is connected to three others by filaments, and when one of them wiggles, so do the others! We're thinking about how to construct a permanent version of this - the current thing is made out of straws and coffee stirrers, but it would likely be more effective to use a solid (perhaps translucent) object in the center, with attachments to surrounding tetrahedra that would allow them to rotate quite freely, perhaps using taut string to connect them together. My department has a 3D printer, which could be useful for making stuff. Last week, I also went to a talk about literature and climate change - one thing they stressed there is that science-art collaborations can and should be much wider in scope than just "using art to explain science", which I confess I had mainly been thinking of this as. Hopefully we can do some deep artistry here! Lizzy's update So this week, Mark took over the duty of creating a model to show. He made another dynamic straw and coffee stirrer masterpiece that offers a glimpse of the jitterbug-rotating effect. From our e-mails, Mark says: Cosmologically, what this represents is the set of galaxies around a void. If a tetrahedron turns in the toy, that represents a change of spin in the galaxy. At least in my origami approximation, the spin of one galaxy would be correlated to other galaxy spins on this network, which I think is pretty cool! I think this is pretty cool, too! Mark’s post this week explains this connection again in his own words. It looks like we will be exploring this idea further, potentially creating a final-product-type model in more refined materials, which may have a different overall geometry than the current model showing tetrahedra. I made a GIF of Mark’s video showing just the rotation effect: https://media.giphy.com/media/QnvDFTzaIKdag/giphy.gif In response to Mark’s final mention in his post this week regarding the breadth and depth of sciart collaboration, here’s a snippet of what I sent him in an e-mail: In my own nascent career, and in watching my role models, I've seen the truth and value in [the sentiment that collaborations can and should be more than just “using art to explain science”]. There's using art to communicate science, and then there's deeper forms of collaboration and communication. I mean, no one ever really talks about using science to communicate art, but it's there too! I've read a few papers on optics studies in Renaissance painting, (there are books on the topic), and there's a substantial theory out there called with Hockney-Falco thesis that claims to have scientifically explained optical effects in the paintings of that time, and how they were able to be so accurate and lifelike. But if you've read any of this year's SciArt Magazine, you'll see glimpses into the more advanced players in the field... They don't just explain something with their work, although sometimes it can serve that role. The work juggles the roles of explaining, raising awareness, and offering poetic insight. Central to poetics and literature is the metaphor. I see myself and other sci-artists oftentimes creating visual metaphors, whether we call it that or not. There's a visual comparison between two unrelated things, that opens up a third space for a completely new perspective on either or both things referenced. It's end result is obviously less "valuable' than a purpose-based creation, in the same way that creations of literature and poetry are often overlooked as frivolous, and yet, they can communicate ideas to the people, and can take the world by storm, in a way that I've never seen any scientific discovery do, at least in my lifetime… Mark and I are in different time zones, which makes meeting for a video chat a little challenging. We’ve been doing okay e-mailing back and forth, but I’m looking forward to some phone calls and more video chats. I hope the above snippet of e-mail correspondence gives you some insight into our communication and thought process! Upon realizing this was the first time Mark had really thought about the importance of deeper collaboration, I’ve let him know a little about my artistic process and how it relates to science in general. I said the process goes something like this, “come up with an idea for a creation [hypothesis], model it [design a and execute an experiment], gauge its success [record results], and either recreate it and refine it, or move onto the next hypothesis [or observation]!” The scientific method is, understandably, taken for granted by those working in science. The methods of artists are less known, and SciArt Magazine does a great job of bringing them to the surface! Our processes, as sci-artists, are often very related and overlapping. From the April 2016 issue, Straight Talk with Jessica Angel: JA: Most importantly, I have discovered that I am not alone developing the ideas I am interested in, and that there are multiple perspectives… When collaborating with people from different disciplines, my spectrum of understanding expands. … so if I could be an enabler for these seemingly different disciplines to collide into an all-inclusive vision of art, I would feel very accomplished…” I couldn’t have said it better myself, Jessica!
Check-in next week… Lizzy's update Mark and I are already working on some different ideas involving his work on the dark-matter sheet. I had a fun time digging into some of his publications as well as reading up on dark matter. We’re planning on creating some visualizations that can provide insight into the weirdness of the multidimensional matter that pervades the universe. We shared some inspirations and past projects to get our gears turning. Mark shared with me a remarkable documentary on origami and folding that he was featured in. Unfortunately, it’s only available for purchase, but I would say it’s worth it. It’s in French, and it’s called “Un monde en plis - Le code origami”. It details the ways in which various disciplines have learned to look to origami, with topics such as protein folding, biological growth, and Mark’s mention on cosmology. I shared with him a documentary on a singular paper folder by the name of Ron Resch. Mark mentioned he had read sources that cite Resch’s work, but had done any further investigating. This one is called “Paper and Stick”: The Ron Resch Paper and Stick Film from Sheet on Vimeo. I’ve only just seen the wonderful stick models that Mark created to model the dynamics of tetrahedral collapse, a 3D twist fold developed to show an idealized version of dark matter halo formation. His portion of this week's blog shows some images of 2D twist folds as well as shares his animated tetrahedral collapse models. He also shares the blog post from 2011 when I worked on an in-class collaboration with artist and designer Dennis Dreher at Rhode Island School of Design. This is what I thought of when Mark mentioned wanting to model a web of nodes undergoing 3D twist folds: to show what cosmologists think happened at the very beginning of the universe. Tiny fluctuations in the nearly uniform early universe caused dark matter to fold up in denser regions, and expand in void regions, leading to the aggregation of matter in the denser regions, where galaxies form. Dark matter comprises about 27% of the matter and energy in the observable universe, with dark energy taking up a whopping 68%. It turns out most of the universe is strange and invisible to electromagnetic detection! I will be creating some models to share for next post! Mark's update Lizzy and I are discussing some practicalities of making a 3D "cosmic web" of nodes ... In a 2D "Flatland" universe, it's possible to simulate a cosmic web with origami, using origami "twist folds", like in the below picture. The top row shows "crease patterns" for the origami, that gets folded up as in the bottom row. Each triangular node schematically corresponds to a galaxy. A 3D twist fold (more relevant to our 3D universe!) is pretty difficult to imagine, unfortunately, and I hope our collaboration can help to get that idea across! In 2D, a twist fold generates structure ultimately by turning a shape, like a triangle as in the above example. 3D twist folds similarly generate structure by rotating a solid by some 3D angle. One such version is below on the left, and a version that doesn't rotate but just inverts is below on the right. In that, the surfaces represent "creases" along which space is folded from the initial to final state.
This weekend, I constructed versions of the "folded" and "unfolded" states of the latter design (the non-rotating, inverting twist fold) out of straws of different thicknesses: red coffee stirrers, and black straws. The straws represent the edges of creases in the above movies ... I made a little movie trying to show their 3D structure (see above). The larger, "folded" state is sort of possible to figure out, but the smaller, "unfolded" state is very hard to figure out and just looks like a jumble of straws! Definitely some work is necessary to get something readily comprehensible out of this! Lizzy introduced me to the idea of "jitterbugs"; it would be awesome to make a jitterbuggy version of one of these cosmic web networks, if possible! Here's a blog post and video of such a jitterbug project that she participated in herself:
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Lizzy Storm is an artist and owner of Lizzy Storm Designs based in Atlanta, Georgia.
Mark Neyrinck is an award-winning astrophysicist and cosmologist, and a postdoctoral researcher at Durham University, United Kingdom.
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