New Visuals for a “New Home”

Takens Theorem
6 min readSep 16, 2022


This series of visualizations depicts data from the perspective of an observer who is embedded in some way in that data. The tokens are both inspired by and part of the “New Home of the Heartcurated collection to commemorate The Merge and its developers and contributors.

Often data is depicted as apart from the observer, such as on a two-dimensional plane, like a graph. It is held at arm’s length. Away from the self. This series asks the observer to imagine themselves intrinsically situated relative to some data, from a given perspective.

This exercise can alter one’s sense of scale and dimension, sometimes in imposing or mysterious ways. These visuals are tightly tied to raw data, but yield some conceptual expression that goes beyond it — from that arrangement of data alone.

(See the accompanying JPG gallery.)

The Merge

These three tokens for “New Home” pertain to The Merge, and they use simple, stark sentiments many of us felt leading into it—excitement, enticement, mystery. What future is beyond TTD 5.875e22? We can envision The Merge with brilliant, vibrant and colorful complexity. But my aim here is to express a curious cognitive dissonance for many of us while we watched the Ethereum wizards work. The Merge gave us a feeling of imposing potential that is uncertain and mysterious and exciting. Bright energy, about to go off, on the backdrop of that alluring and unknown future.

Here are three new 1/1s, “Portal” (token #1), “Next” (token #2) and “Engine” (token #3), released on my new Manifold contract for “New Home of the Heart.” The owner of “Portal” will receive “Next” and “Engine” as a set. You can bid on the complete set of 3 on the JPG minting site.


20,000 x 20,000 pixels, JPG, ~20 MB
Click here to see the full-size asset on Arweave
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An observer at the precipice of The Merge. The observer turns, looking back at history. Rings represent dates, their area proportional to the TTD on that date going back in time. An array is interconnected by markers with areas proportional to the average difficulty on that ring’s day: mass energy supporting an unbroken chain extending back years.

Variation on “Portal” is rendered entirely deterministically from data with only adjustments to get it precisely into view. An important ingredient here is to make data seem spatial — time is extending back in space, too. To do this, I scaled the raw data by time in a manner that physical objects do in space, using the size/distance quotient (in essence, dividing the scale that occupies view by its remoteness in time). Opacity and y-axis are scaled by time as well, to give this data the feel of visuospatial depth, a history extending back from the observer. (Resizing these views can create a sparkling aliasing, star-like shapes in the overlapping rings, echoing again the underlying idea of an energy-consuming landscape.)

Despite this edifice, change is upon the observer. The structure is at its last ring, off like a switch.

“Portal” depicts the observer about to escape this energy-consuming reticulum into something beyond. You can imagine the observer turning, looking beyond the last ring.

What’s next?


20,000 x 20,000 pixels, JPG, ~8 MB
Click here to see the full-size asset on Arweave
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At the edge of sheer potential, what’s next?

Here we have transaction data from GENESIS to the edge of the PoW Ethereum network, an unbroken chain supported by mass energy. I sampled 50 wallets from GENESIS (including the Ethereum Foundation’s originating source of ether), and sampled from their transactions. I then sampled from their recipients as ether (and calls) flowed through the network. Iterated sampling of wallets and their recipients transitively generates a chain of transactions from GENESIS to beyond the 15,000,000th block, into our era of The Merge. Over 30,000 transactions, and 10,000 wallets are depicted here. A mere glimpse.

The network in “Next” is depicted from a “bird’s-eye” perspective of what may be. The Merge is just the start of several upgrades meant to bring scale and efficiency. The area occupied by the graph is an order or two magnitude smaller than what may be possible, selected to be about 1% of the visual’s dimensions. Scaling upgrades and their applications, if successful, have one or even two orders of magnitude to expand into the daily financial behavior of billions of people. Ethereum represents a scalable open system for countless new experiments and opportunities.

The 20,000² image shows our present state as a relatively small proportion of this possible future.

Zoom into “Next”
Zoom into “Next”


10,000 x 10,000 pixels, JPG, ~25 MB
Click here to see the full-size asset on Arweave
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In my 2021 series “Ethstory,” visualizing the history of Ethereum, I used code as a medium for expressing various aspects of Ethereum’s history. For example “Clients” and “64 Shards” use the execution layer code (Eth1) and consensus layer code (Eth2) to “stitch” patterns that express particular technical and historical aspects about Ethereum.

“Engine” uses this theme again, but takes all data sources from those two pieces in “Ethstory.” On the left quadrants of “Engine,” the early codebase for the two execution clients (left-top: geth, left-bottom: parity); on the right quadrants, early codebase for two consensus clients (right-top: lighthouse, right-bottom: prysm). I extracted source files from early GitHub releases, sequenced them with a bit of filtering and portioning for length, then wrapped them into loops consecutively, from the center out to each corner. They overlap at quadrant edges. Admittedly, there is some aesthetic license here apart from the code. But it has a purpose in concluding this three-piece sequence.

The first two pieces of “New Home” navigate mystery and uncertainty in The Merge—an uncertain future of great potential. The observer is at the edge of a massive network, then looking down on what is possible. In “Engine,” the observer now narrows their view, focusing, zooming in — inside, observing the machinery of the system. Components from the distributed system are weaving together, communicating. A small energy signature, microscopic compared to rings of “Portal,” but rich and complex in their activity.

Ethereum will navigate this space with a new engine. The code comes together. The result is a bright, churning computational core, whirling embers of a complex governor engine. Still with the backdrop of the prior two, but glowing distributed communication fusing its parts. Not so much energy now as coordination.

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I’ve also explored fully on-chain visualization, such as Gaussian Timepieces (2021), a dynamic NFT exploring stochasticity in blockchain time; and The Mesh (2022), a dynamic NFT that interconnects all collectors on the contract.

See my website for more projects and writing.



Takens Theorem

Dynamic distributed data displays. Intermittent. Friendly.