I was surprised too, but I have no experience with these measures.
I imported the image into Mathematica, summed the total brightness across all three colour channels at 10,000 points at the centres of the squares in the grid, and normalised to a sum of 1, to get the probabilities p_i.
Then I used:
H = –Σ_i p_i log_2(p_i)
with the summand being 0 when p_i = 0.
I checked the data by turning it back into a grayscale image, and it looks just like the original to my eye.
So if I’ve made a mistake, it’s hard to see what I’ve done wrong.
Greg Egan
npub12c…gd38p
2025-01-28 00:09:21 UTC
in reply to nevent1q…tpsz
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pPublished at
2025-01-28 00:09:21 UTCEvent JSON
{
"id": "7a8c4edcb62374ac9cbdf57541f7da1b121eaab1bcb268551f6e4ac1ca3d9c15",
"pubkey": "563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3",
"created_at": 1738022961,
"kind": 1,
"tags": [
[
"e",
"c48f64133c7e4be05c67b0ce5273f12ff952f332d5b5f7482131a55f740237a0",
"",
"reply",
"378fb8535da3c841fdebd0966e5a16f3d21d4e988b925e471f2d8fdf2345d2e9"
],
[
"p",
"563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3"
],
[
"proxy",
"https://mathstodon.xyz/@gregeganSF/113903072801172742",
"web"
],
[
"e",
"826a992b70ed67547e423a305103e3d0bffa116004216776e6ec558be2eccbd4",
"",
"root",
"563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3"
],
[
"p",
"378fb8535da3c841fdebd0966e5a16f3d21d4e988b925e471f2d8fdf2345d2e9"
],
[
"proxy",
"https://mathstodon.xyz/users/gregeganSF/statuses/113903072801172742",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/gregeganSF/statuses/113903072801172742",
"pink.momostr"
],
[
"-"
]
],
"content": "I was surprised too, but I have no experience with these measures.\n\nI imported the image into Mathematica, summed the total brightness across all three colour channels at 10,000 points at the centres of the squares in the grid, and normalised to a sum of 1, to get the probabilities p_i.\n\nThen I used:\n\nH = –Σ_i p_i log_2(p_i)\n\nwith the summand being 0 when p_i = 0.\n\nI checked the data by turning it back into a grayscale image, and it looks just like the original to my eye.\n\nSo if I’ve made a mistake, it’s hard to see what I’ve done wrong.",
"sig": "70adecbdf1cd1da21a9c4d6ae8917c818720e6758337a5d63e14f7e32a132d92090b8988987de6c3ca024ded7189fa012e898c9313ac249b13822b58e84a896a"
}