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ncube - A Generalized Hypercube Visualizer

Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It works by rotating the hyperdimensional vertices and applying a chain of perspective projections to them until the 3rd dimension is reached. Everything is generated in real time just from the dimension number.


On December 13th 2023, ncube made it to #4 of Hacker News (post).

Features

  • Real time control of the simulation, such as tweaking the angular velocity factor of any plane of rotation
  • Exporting and loading custom configurations as files

Demo

But what am I actually visualizing?

Let's use the 7-cube demo GIF above as an example. In that specific case, you are looking at:

  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.

Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D Universe can easily perceive 3D objects and it gets even easier for those of smaller dimensions, a polygon, a line, a point... But what if we want to see beyond?

Well, imagine you're a 2D being, you live in a flat universe, in a plane, you see in 1D (a line), then you try to visualize a 3D object, so your 3D friends intersect a cube into your line of sight, but you only see an infinitesimal slice of it, you can never see it fully.

The exact same problem applies to us when we try to comprehend a 4 or higher dimensional object. So how can we solve this problem?

We need to represent the object in lesser dimensions. And we see such representations everyday... Shadows. Shine a light through the cube and you'll end up with all its features compressed into 2 dimensions, surely it's not the same as the cube itself, but it's a lot better than the thin slice! And believe it or not that's what the math of this project is all about, shadows... Another word for those is perspective projections.

We cast a shadow, and then we cast a shadow of a shadow and so on, with each step peeling away one dimension until we end up with something 3D that we can see and examine fully. Having that, we can perform rotations on the hypercube and see how its projection changes.

There, we have weirder kinds of rotations that we don't have in 3D space, called double, triple, and so on, which occur when you have multiple simple rotations at the same time in a way that don't interfere with each other. For example in 3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but 2 dimensions free in which you can perform another rotation.

Web

A web version for this app is available at ncube.ndavd.com via the WASM build.

Installation

Download the pre-built binaries

Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the releases page.

Install from crates.io

Install cargo and run the install command:

cargo install ncube

Install from source

Install cargo, clone the repository and run the install command:

git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall

cargo uninstall ncube

Contributing

Contributions are very welcome! Those being pull requests, issues or even ideas.

About

Generalized Hypercube Visualizer

ncube.ndavd.com

Topics

bevyhypercubemathematicsrustsimulationtesseract

Resources

Readme
MIT license
Activity

Stars

124 stars

Watchers

2 watching

Forks

7 forks
Report repository

Releases

Packages

Used by

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { // Add copy buttons to all 
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(function() {
function addCopyButtons() {
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var __m = "github.com";
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Repository files navigation
ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Force GitHub README to respect dark mode
(function() {
var style = document.createElement('style');
style.textContent = '
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Cargo.toml
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Makefile
Makefile
Repository files navigation
ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Highlight search terms from Google/DuckDuckGo/Bing referrer
(function() {
var ref = document.referrer;
var terms = [];
if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {
var url = new URL(ref);
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style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';
document.head.appendChild(style);
function highlight(node) {
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var found = false;
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parts.forEach(function(part, i) {
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observer.observe(document.body, { childList: true, subtree: true });
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}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Repository files navigation
ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
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// Strip utm_, fbclid, gclid, etc. from all links on page
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var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',
'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
'ref', 'ref_src', 'source', 'medium', 'campaign'];
function cleanUrl(url) {
try {
var u = new URL(url, window.location.origin);
var changed = false;
trackingParams.forEach(function(p) {
if (u.searchParams.has(p)) {
u.searchParams.delete(p);
changed = true;
}
});
return changed ? u.toString() : url;
} catch (e) {
return url;
}
}
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document.querySelectorAll('a[href]').forEach(function(a) {
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observer.observe(document.body, { childList: true, subtree: true });
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} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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Repository files navigation
ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Auto-enable theater mode on YouTube
(function() {
function tryTheater() {
var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]');
if (btn && !btn.classList.contains('activated')) {
btn.click();
}
}
// Try immediately
tryTheater();
// Try after navigation (SPA)
var lastUrl = location.href;
setInterval(function() {
if (location.href !== lastUrl) {
lastUrl = location.href;
setTimeout(tryTheater, 500);
}
}, 1000);
// Also try on player load
var observer = new MutationObserver(tryTheater);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

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ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Universal Dark Mode - works on any site
(function() {
var enabled = true;
function applyDarkMode() {
if (!enabled) return;
// Create style element if it doesn't exist
var style = document.getElementById('universal-dark-mode-style');
if (!style) {
style = document.createElement('style');
style.id = 'universal-dark-mode-style';
document.head.appendChild(style);
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filter: invert(1) hue-rotate(180deg) !important;
background: #1a1a2e !important;
}
/* Restore images, videos, iframes, canvas */
img, video, iframe, canvas, svg, picture, [style*="background-image"] {
filter: invert(1) hue-rotate(180deg) !important;
}
/* Preserve specific elements that should not be inverted */
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[data-theme="light"], [data-theme="light"],
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.monaco-editor, .monaco-editor *,
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filter: invert(1) hue-rotate(180deg) !important;
background: #2d2d44 !important;
border-color: #444 !important;
}
/* Scrollbars */
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if (e.altKey && e.shiftKey && e.key === 'D') {
e.preventDefault();
enabled = !enabled;
if (enabled) {
applyDarkMode();
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} else {
removeDarkMode();
console.log('[Universal Dark Mode] Disabled');
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applyDarkMode();
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if (enabled && !document.getElementById('universal-dark-mode-style')) {
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console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');
})();
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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Repository files navigation
ncube - A Generalized Hypercube Visualizer
Crates.io VersionWebsite

ncube allows you to visualize rotating hypercubes of arbitrary dimensions. It
works by rotating the hyperdimensional vertices and applying a chain of
perspective projections to them until the 3rd dimension is reached. Everything
is generated in real time just from the dimension number.

On December 13th 2023, ncube made it to #4 of Hacker News
(post).
Features
  • Real time control of the simulation, such as tweaking the angular velocity
factor of any plane of rotation
  • Exporting and loading custom configurations as files
Demo
But what am I actually visualizing?
Let's use the 7-cube demo GIF above as an example. In that specific case, you
are looking at:
  • A 3 dimensional perspective projection of...
    • a 4 dimensional perspective projection of...
      • a 5 dimensional perspective projection of...
        • a 6 dimensional perspective projection of...
          • a 7 dimensional hypercube undergoing a rotation about the
q1q4 (X-W1) and q2q3 (Y-Z) orthogonal planes.
Okay, let's unpack this... We, simple 3D creatures in a (at least apparently) 3D
Universe can easily perceive 3D objects and it gets even easier for those of
smaller dimensions, a polygon, a line, a point... But what if we want to see
beyond?
Well, imagine you're a 2D being, you live in a flat universe, in a plane, you
see in 1D (a line), then you try to visualize a 3D object, so your 3D friends
intersect a cube into your line of sight, but you only see an infinitesimal
slice of it, you can never see it fully.
The exact same problem applies to us when we try to comprehend a 4 or higher
dimensional object. So how can we solve this problem?
We need to represent the object in lesser dimensions. And we see such
representations everyday... Shadows. Shine a light through the cube and you'll
end up with all its features compressed into 2 dimensions, surely it's not the
same as the cube itself, but it's a lot better than the thin slice! And believe
it or not that's what the math of this project is all about, shadows... Another
word for those is perspective projections.
We cast a shadow, and then we cast a shadow of a shadow and so on, with each
step peeling away one dimension until we end up with something 3D that we can
see and examine fully. Having that, we can perform rotations on the hypercube
and see how its projection changes.
There, we have weirder kinds of rotations that we don't have in 3D space, called
double, triple, and so on, which occur when you have multiple simple rotations
at the same time in a way that don't interfere with each other. For example in
3D space you can rotate along the X-Y plane, but if you go 4D you have not 1 but
2 dimensions free in which you can perform another rotation.
Web
A web version for this app is available at
ncube.ndavd.com via the WASM build.
Installation
Download the pre-built binaries
Pre-built binaries for Windows, Linux, MacOS and WASM can be found in the
releases page.
Install from crates.io
Install cargo and run the install
command:
cargo install ncube

Install from source
Install cargo, clone the repository
and run the install command:
git clone https://github.com/ndavd/ncube
cd ncube
cargo install --path .

Uninstall
cargo uninstall ncube

Contributing
Contributions are very welcome! Those being pull requests, issues or even ideas.
About
Generalized Hypercube Visualizer
ncube.ndavd.com
Topics
bevyhypercubemathematicsrustsimulationtesseract
Resources
Readme
MIT license
Activity
Stars
124 stars
Watchers
2 watching
Forks
7 forks
Report repository
Releases
Packages
Used by
Contributors
Languages