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Tom Lowe

Tom Lowe Add us as a preferred source on Google

Mastodon @toml@mathstodon.xyz
⚔ Compare ☆ Follow Own this channel?
🔄 Data last refreshed 2 days ago
Followers
213
Account age
2 yrs
🎁 Free analysisfor Tom Lowe
🕵️Fake Followers CheckReal-audience % & bot risk→ 📊Engagement rateBenchmarked vs. peers→ 💰What they chargeFair sponsored-post price→

Known for

Here's a 600-cell inversive limit set. This is a set that is invariant to inversions around spheres centred at the 600-cell's vertices, and stereographically projected into 3D. The spheres must meet at a dihedral angle of π/𝑛 for some integer 𝑛. So there are a countably infinite number of such shapes, however there are three that are the key ones: 𝑛=3: the set complement of a ball packing. 𝑛=4: 10 views Here's a 600-cell inversive limit set. This is a set that is invariant to inversions around spheres centred at the 600-cell's vertices, and stereographically projected into 3D. The spheres must meet at a dihedral angle of π/𝑛 for some integer 𝑛. So there are a countably infinite number of such shapes, however there are three that are the key ones: 𝑛=3: the set complement of a ball packing. 𝑛=4: Here's the 𝑛=∞ case. Both have a tetrahedral rotational symmetry, that's because the cells of the 600-cell are tetrahedra. While these are stereograpic projections of objects in 4D, they aren't themselves 4D objects. They are subsets of the 3-sphere. I prefer to think of them natively in 3D. So rather than just a projection from a shape in 4D they are a 'conformal type' in 3D. While a shape is 7 views Here's the 𝑛=∞ case. Both have a tetrahedral rotational symmetry, that's because the cells of the 600-cell are tetrahedra. While these are stereograpic projections of objects in 4D, they aren't themselves 4D objects. They are subsets of the 3-sphere. I prefer to think of them natively in 3D. So rather than just a projection from a shape in 4D they are a 'conformal type' in 3D. While a shape is This limit set is different to other substitution limit sets (https://www.researchgate.net/publication/407295122_Inversive_Substitution_Systems) the blue and green tree limbs interlock a little, overlapping each other's space. This normally doesn't happen in escape-time limit sets because the geometry is local to individual spheres. So to support it the distance estimator needs to make a new iter6 views This limit set is different to other substitution limit sets (https://www.researchgate.net/publication/407295122_Inversive_Substitution_Systems) the blue and green tree limbs interlock a little, overlapping each other's space. This normally doesn't happen in escape-time limit sets because the geometry is local to individual spheres. So to support it the distance estimator needs to make a new iter The above example was a tree-cluster-tree. A cluster-tree is like the Mandelbrot set, lots of dense balls that kiss in a tree structure (acyclic connectivity). A tree-cluster-tree is the same but the dense balls are trees. Anyway, here's a similar example but with just a tree structure. The limbs are non-aligned, and there's a bit of overlapping of each set's space. I suspect that this method cou5 views The above example was a tree-cluster-tree. A cluster-tree is like the Mandelbrot set, lots of dense balls that kiss in a tree structure (acyclic connectivity). A tree-cluster-tree is the same but the dense balls are trees. Anyway, here's a similar example but with just a tree structure. The limbs are non-aligned, and there's a bit of overlapping of each set's space. I suspect that this method cou

📊 Post engagement

Recent posts · likes + reposts
Apr 22latest
5
Avg engagement / post
4–6
Typical post (engagement)
2.3%
Engagement vs followers
80/100
Very consistent reach
Sep 2024
On Mastodon since
Half of recent posts land between 4 and 6 likes + reposts (median 4) — a dependable floor a sponsored post can count on.

🔥 Top post: Here's a 600-cell inversive limit set. This is a set that is in · 10 likes + reposts

📊 Activity & format

Posting cadence
1.3 / week
A lower-frequency account — each post lands with more weight.
Content mix
Mostly images
Recent: 1 text · 9 image · 2 video.
Follower / following
0.8×
Follows 268 back. A more reciprocal / networked account.

Recent posts

View on Mastodon ↗
▶ 🔥 Top post Here's a 600-cell inversive limit set. This is a set that is invariant to inversions around spheres centred at the 600-cell's vertices, and stereographically projected into 3D. The spheres must meet at a dihedral angle of π/𝑛 for some integer 𝑛. So there are a countably infini… ★ 10
The above example was a tree-cluster-tree. A cluster-tree is like the Mandelbrot set, lots of dense balls that kiss in a tree structure (acyclic connectivity). A tree-cluster-tree is the same but the dense balls are trees. Anyway, here's a… ★ 5 This was built from a basic octahedral set (grey) with two spheres added on its left hand side. To get interlocking limbs that don't join to a sponge we need to substitute each coloured sphere with the set minus its opposing sphere. So the… This limit set is different to other substitution limit sets (https://www.researchgate.net/publication/407295122_Inversive_Substitution_Systems) the blue and green tree limbs interlock a little, overlapping each other's space. This normal… ★ 6 The least dense needs a little work to render it nicer, but this is the shape. The realtime renderer is here: https://www.shadertoy.com/view/sXlGWs (3/3) ★ 3 The 5-cell, 8-cell, 16-cell and 24-cell inversive limit sets are in the void-sponge class here: https://www.shadertoy.com/view/cslfWn The last of the regular polychora is the 120-cell. This the last as it has 600 vertices, which is a bit t… ★ 4 There is a denser 600-cell inversive limit set if we break the rules and allow half-integer orders. This is the densest that isn't the complement of a ball packing, at 𝑛=3.5. It isn't really breaking the rules, the dihedral angle between s… ★ 5 600-cells are interesting, their usual choice of 4D vertices can also be interpreted as quaternions 𝑞ᵢ, and since a rotation in 4D is specified by two quaternions, we can get all of the symmetries of the 600-cell by applying all combinatio… ★ 4 ▶ Here's the 𝑛=∞ case. Both have a tetrahedral rotational symmetry, that's because the cells of the 600-cell are tetrahedra. While these are stereograpic projections of objects in 4D, they aren't themselves 4D objects. They are subsets of … ★ 7 The last method needs a tweak, the little green patches do need the transition (dull yellow) tile between them and the larger brown patch. But with that in place it seems to be solidly continuous. Here I'm stress testing it by changing the… ★ 2 With the overlap limit set placed between them we have a continuous landscape. It also removes ambiguity of which child set has priority at the overlap. The overlap constraints leave four free spheres that can be adjusted on this overlap … ★ 4 The second problem is that the terrain patches are all separated disks which is also unnatural. That's because you can't apply a substitution to two neighbouring spheres, or it causes discontinuities. This is solvable but it is a bit tric… ★ 3

🐘 Community & instance

Home server
mathstodon.xyz
Their home server on the fediverse — the instance a creator picks signals the community they belong to.
On Mastodon since
Sep 2024
An established account with real history on the platform.

💡 Facts

🗓️Joined Mastodon in 2024 — 2 years ago.
👁️Averages 5 views per post.
📤Posts about 1.3× per week.

🕵️ Fake follower check

Estimated
61/100
Fair Credibility score
84%
Real Real audience
Low Fake-follower risk
High Data confidence
  • Est. 84% real, active audience · Low fake-follower risk.
  • Engagement (~2.3% of followers engage each post) is around typical for Mastodon.

Heuristic estimate from engagement, follower ratios, account age & growth — a screening signal, not a guarantee.

About

I'm interested in Computer Graphics, Geometry, Mathematics and Physics. I have worked in Games Development, Animation Development, and now in Robotics Development, I guess that makes me a developer. Vous pouvez me parler dans n'importe quelle langue, c'est assez facile à traduire en ligne si je ne le connais pas.

📸 Gallery

The above example was a tree-cluster-tree. A cluster-tree is like the Mandelbrot set, lots of dense balls that kiss in a tree structure (acyclic connectivity). A tree-cluster-tree is the same but the dense balls are trees. Anyway, here's a similar example but with just a tree structure. The limbs are non-aligned, and there's a bit of overlapping of each set's space. I suspect that this method cou This was built from a basic octahedral set (grey) with two spheres added on its left hand side. To get interlocking limbs that don't join to a sponge we need to substitute each coloured sphere with the set minus its opposing sphere. So the green child limit-set lacks the blue sphere and the blue child limit-set lacks the green sphere, as seen here. Because we spin up parallel threads, the green a This limit set is different to other substitution limit sets (https://www.researchgate.net/publication/407295122_Inversive_Substitution_Systems) the blue and green tree limbs interlock a little, overlapping each other's space. This normally doesn't happen in escape-time limit sets because the geometry is local to individual spheres. So to support it the distance estimator needs to make a new iter The least dense needs a little work to render it nicer, but this is the shape. The realtime renderer is here: https://www.shadertoy.com/view/sXlGWs (3/3) The 5-cell, 8-cell, 16-cell and 24-cell inversive limit sets are in the void-sponge class here: https://www.shadertoy.com/view/cslfWn The last of the regular polychora is the 120-cell. This the last as it has 600 vertices, which is a bit tricky to render in real time. I ended up finding a set of vertices with axial symmetry so I only needed to store about a sixteenth of them. Would be faster to u There is a denser 600-cell inversive limit set if we break the rules and allow half-integer orders. This is the densest that isn't the complement of a ball packing, at 𝑛=3.5. It isn't really breaking the rules, the dihedral angle between spheres is still π/𝑛 for an integer n, it is just that the two intersecting spheres aren't both at the 600-cell vertices, instead it is the angle between one of Here's the 𝑛=∞ case. Both have a tetrahedral rotational symmetry, that's because the cells of the 600-cell are tetrahedra. While these are stereograpic projections of objects in 4D, they aren't themselves 4D objects. They are subsets of the 3-sphere. I prefer to think of them natively in 3D. So rather than just a projection from a shape in 4D they are a 'conformal type' in 3D. While a shape is Here's a 600-cell inversive limit set. This is a set that is invariant to inversions around spheres centred at the 600-cell's vertices, and stereographically projected into 3D. The spheres must meet at a dihedral angle of π/𝑛 for some integer 𝑛. So there are a countably infinite number of such shapes, however there are three that are the key ones: 𝑛=3: the set complement of a ball packing. 𝑛=4:

🔀 Audience overlap

Estimated

Estimated shared audience with similar creators — useful for avoiding overlap (or doubling down) when planning a campaign.

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