Before I came here, I didn't know there were people using web pages to demonstrate such cool things.
Show HN: I was curious about spherical helix, ended up making this visualization
131–140 of 140 posts
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#132These used to be super important in early oceanic navigation. It is easier to maintain a constant bearing throughout the voyage. So that's the plan sailors would try to stick close to. These led to let loxodromic curves or rhumb lines. https://en.m.wikipedia.org/wiki/Rhumb_line Mercator maps made it easier to compute what that bearing ought to be. https://en.m.wikipedia.org/wiki/Mercator_projection This configuration…
Jeez Erdos. This man was so prolific he was still publishing 4 years after he died :o
Many after he passed
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#133These used to be super important in early oceanic navigation. It is easier to maintain a constant bearing throughout the voyage. So that's the plan sailors would try to stick close to. These led to let loxodromic curves or rhumb lines. https://en.m.wikipedia.org/wiki/Rhumb_line Mercator maps made it easier to compute what that bearing ought to be. https://en.m.wikipedia.org/wiki/Mercator_projection This configuration…
Except the helix curve shown in OP is NOT a loxodrome or rhumb line. It has equal spacing on the surface between lines, a loxodrome can't have that property since by definition it must cross the meridians at the same angle at all times. That means it always gets denser near the poles. --- Start with the curve: x = 10 · cos(π·t/2) · sin(0.02·π·t) y = 10 · sin(π·t/2) · sin(0.02·π·t) z = 10 · cos(0.02·π·t) Convert to sp…
Indeed. It is one of the many well known spherical spirals / seiffert spirals.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#134> …which we know isn't actually chaotic. It's just a path defined by mathematical functions. I don't know what function is being presented, so I can't speak to whether it demonstrates chaotic behavior -- but the whole /point/ of chaos is that it's an emergent property of deterministic mathematical functions. Perhaps the author meant "random" or "non-deterministic" rather than "chaotic"?
I just did a mental substitution for the word "stochastic" and moved on, since it wasn't the main point of the article. But you are correct. Computing the future states of a chaotic system, given the same initial conditions, will produce the same results every time but change the initial conditions ever so slightly and you have no guarante where you will end up next (unless you picked a state from a previous simulation, that is... But that's cheating;) )
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#135Earlier quoted context omitted.
'actual' or 'true' randomness is a rabbit hole. https://en.wikipedia.org/wiki/Randomness It really depends on the exact definition of what you are quantifying 'random' to be. There is no proof (in the mathematical sense) of real randomness.
I use "Random" to mean chaotic (extreme sensitivity to initial conditions) but with unknown (or unknowable) initial conditions.
I think that makes sense and I can tell that you understand the distinction. Formally I believe they're different concepts and think it may cause confusion in some cases to use them interchangeably.
The chaotic nature of a system is one thing.
Our lack of knowledge of the governing laws, initial conditions, feasibility of simulation forcing us to use the mathematical tools of probability (i.e. randomness) to describe our uncertainty about said system is another thing.
The reason why it matters is that a statement like "a double inverted pendulum behaves randomly" is just wrong as it would imply that you couldn't even do a simulation of one in theory without throwing some dice.
However, it is totally uncontroversial that if someone gave you a measured initial position and velocity of one with 'really good' precision and asked you to predict its state 5 seconds forward you would likely have a big smeared-out probability density function to deal with.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#136this is so pretty. Have you done any write-ups on how to create this (or any of the other visualisations on your page). I would love to learn more.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#137If you like this, you will probably enjoy https://www.shadertoy.com/ and https://thebookofshaders.com/
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#138I applaud anybody who makes visualizations of difficult to grasp concepts - so, thank you very much.
As a visual (spatial) learner, I often wonder how my math/science education could have been improved with learning tools such as these.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#139I can't tell why, but I'm getting terrible performance on Linux/Brave. The CPU spikes immediately on visit. I'm on a powerful machine (32 GiB RAM, Intel i9 w/ 24 cores).
I encountered similar trouble with both Firefox and Chrome on Ubuntu.
Based on a quick Firefox performance report on the minified source code, most of the time seems to be spent in functionality looking like frame handling. There are some signs of time calculations.
One educated guess would be that something in frame time calculations goes off, possibly due to restricted time resolution to prevent timing related fingerprinting. This would cause next frame computation to start immediately instead of after the intended timeout.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#140I can't tell why, but I'm getting terrible performance on Linux/Brave. The CPU spikes immediately on visit. I'm on a powerful machine (32 GiB RAM, Intel i9 w/ 24 cores).
I encountered similar trouble with both Firefox and Chrome on Ubuntu. Based on a quick Firefox performance report on the minified source code, most of the time seems to be spent in functionality looking like frame handling. There are some signs of time calculations. One educated guess would be that something in frame time calculations goes off, possibly due to restricted time resolution to prevent timing related fing…
Frankly, it seems to work fine on Firefox. It's a Brave issue for me.