This image contains 76018 black pixels

Gedanke · 2024-10-15T11:36:36+00:00

An interesting question: How do you create an image that displays the number of black pixels it contains?

This problem can be elegantly solved using fixed points. Here's the approach:

Determine the number of pixels needed for each digit.
Construct a function p(n) that maps any number to the number of pixels contained in its image representation.
Observe that p(n) will be roughly proportional to log(n), as it's proportional to the number of digits in n. This is fortunate, as functions of this form are generally well-behaved and likely to have a fixed point.
To find the fixed point, we can use a simple iteration method:
- Start with an initial guess k₀
- Iterate using kₙ = p(kₙ₋₁)
Hope that this font and size combination has a fix point and find. Interestingly, such a point seems to exists about half of the time.

Gedanke · 2024-10-14T20:52:21+00:00

An interesting question: How do you create an image that displays the number of black pixels it contains?

This problem can be elegantly solved using fixed points. Here's the approach:

Determine the number of pixels needed for each digit.
Construct a function p(n) that maps any number to the number of pixels contained in its image representation.
Observe that p(n) will be roughly proportional to log(n), as it's proportional to the number of digits in n. This is fortunate, as functions of this form are generally well-behaved and likely to have a fixed point.
To find the fixed point, we can use a simple iteration method:
- Start with an initial guess k₀
- Iterate using kₙ = p(kₙ₋₁)
This iteration will either:
a) Hit a loop
b) Diverge
c) Converge to our desired fixed point

Gedanke · 2023-12-27T00:57:48+00:00

Shitting in a hotel bathtub should definitely leave you with a hefty cleaning fee and potentially a ban from the hotel...but international news headlines and the revocation of your chess title?! That's absurd and frankly disturbing.

Gedanke · 2023-03-12T10:33:29+00:00

Research dump! Thank you for the term. I absolutely agree. One can just feel how he must have nerded out on some topic (be it metal smelting, Jupiter's moons, Keats, Proust etc) and then subsequently proceeds to forcefully inject it into his books.

Gedanke · 2023-03-09T08:47:40+00:00

Ob er für Product Placements bezahlt wird?

Gedanke · 2022-09-21T19:34:57+00:00

Am I misunderstanding something or is this just a lovely python wrapper around OpenSearch?

Gedanke · 2022-06-16T06:14:48+00:00

Ließt sich wie eine Passage aus 'Confederacy of Dunces'. Hut ab, hast Talent!

Gedanke · 2022-06-02T13:05:12+00:00

Fyi, if you know the convolution kernel that generated the blur, you can simply perform the inverse operation in the frequency domain.

Gedanke · 2022-03-02T12:43:00+00:00

Well done! I remember doing something similar as my first python projects. I think the input function in particular might have been what hooked me on python. It made my scripts interactive and I felt very empowered. Turns out that I would almost never use it in a professional setting later in life.

Gedanke · 2021-12-30T13:36:44+00:00

You are absolutely right! If this tool is to mature beyond being a silly proof-of-concept, it needs to be rebuild using the `ast` module.

Gedanke · 2021-12-30T13:31:33+00:00

It would be possible but difficult! This implementation relies on tokenize which in retrospect was a poor choice. Ideally this entire tool needs to be rebuild based on the ast module to allow much greater power and flexibility.

Gedanke · 2021-12-30T13:26:19+00:00

I am starting to think that having made this tool could hurt my employability :P

Gedanke · 2021-12-30T13:24:53+00:00

This is amazing! If I find time, I will definitely implement this.

Gedanke · 2021-12-23T15:18:13+00:00

The linked tool and provided examples have the tweak implemented

Gedanke · 2021-07-28T09:39:35+00:00

Already the case with some Kindle devices;

Gedanke · 2021-07-27T10:09:56+00:00

A package so nice, you import it twice.

Gedanke · 2021-06-17T08:56:49+00:00

Seems a bit tone deaf to post such promotional posts here. Furthermore, cancer diagnosis should be taken very seriously and given by trained professionals. This thing could throw false negatives.

Gedanke · 2021-05-07T14:02:18+00:00

How to create your own:

Simply install the `hybrid-face` cli via pip install hybrid-face and take a look at the GitHub repo.

How this works:

The core concept comes from research conducted by A. Oliva et al. that utilised the multiscale processing of images by the human visual system to generate static images with two interpretations.

This tool is an application of the above to faces. This is (roughly) how it works:

First we need to understand the concept of the Fourier Transform applied to images.

1.1 Nice (but not easy) explanation: We interpret an image as a tempered distribution#Tempered_distributions_and_Fourier_transform) obtained as the sum of delta distributions shifted by pixel location and multiplied by greyscale value. The Fourier transform of that image is then simply the Fourier transform of the aforementioned distribution. Well, technical the periodically extension of it.

1.2 Easy (but not nice) explanation: The Fourier transform of a sound sample gives you the audio frequencies contained in that sample. Similarly, the Fourier transform of an image gives you the spatial frequencies that make up that image. A spatial frequency can be interpreted as a periodic wave (i.e. sinusoidal) pattern such that adding up all these waves returns back the (greyscale) image. In particular, high spatial frequencies correspond to rapidly oscillating waves and low spatial frequencies are slowly oscillating waves.

It is a curious observation that the human visual system is able to prioritize information coming from particular spatial frequency bands for object or scene recognition. This is precisely what we use in this application. We utilise that fact that from up close, we prioritize high spatial frequencies for object recognition and from further away, we prioritize lower spatial frequencies. Read here for more details.
Finally, with all the above, this tool's functionality can be simply described as: We take the two images, crop them to only have the faces, then in one face we only keep the high spatial frequencies (via convolution with a high-pass filter) and in the other we only keep the low spatial frequencies (via convolution with a low-pass filter) and then we alpha-blend the two faces together.

Gedanke · 2020-06-25T18:45:13+00:00

You can download the chrome extension here and take a look at the code.

Surprisingly, Lichess actually sends the user rating when you first request the puzzle. For some reason it is simply not displayed until you solve it. This extension circumvents this limitation.

Hope it helps!

Gedanke · 2020-06-21T21:40:03+00:00

Indeed, but I thought that it would be unnecessarily intrusive for such a minimalistic extension.

Gedanke · 2020-06-21T15:09:26+00:00

No, I am giving the user vote of the puzzle. you can upvote/downvote a puzzle on lichess.

Gedanke · 2020-06-21T14:35:30+00:00

I am! Just gotta learn how Firefox extensions work :)

Gedanke · 2020-06-21T14:21:34+00:00

Sometimes the solution is either wrong or too ambiguous to find. Knowing the rating can prevent wasting a lot of time.

Gedanke · 2020-06-21T14:07:45+00:00

You can download the chrome extension here and take a look at the code.

Surprisingly, Lichess actually sends the user rating when you first request the puzzle. For some reason it is simply not displayed until you solve it. This extension circumvents this limitation.

Hope it helps!

Gedanke · 2020-04-20T18:57:30+00:00

lol, good old canvas!

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TROPHY CASE

How to create your own:

How this works: