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ojovivo
Mike Driver
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JBB: An Artblog!
#extradirty
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if i look back, i am lost
Cosmic Funnies
$LAYYYTER
Alisa U Zemlji Chuda
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Keni
blake kathryn
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Today's Document
ellievsbear
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@madeofkaons
welcome to my blog!
(I figured it was about time I made an introduction, as I've been here a while now.)
hello there, I'm madeofkaons, or just kaon for short. I also go by kmesons in some places. I'm a bit of a math and science nerd and post semi-regularly here about that kind of thing.
I also do art and make posts related to my favourite media, which you can find on my sideblog, @kmesons.
there are infinitely many primes (topological proof due to Furstenberg)
Aroace shapeeeeeees
mathematics is a sort of goo/ooze secreted by human minds when they rub against a universe
#and so is art
guys check it out I'm gonna evaluate the limit of this rational function
l'hôpital
Let's start a thread where we collect papers with funny titles. I'll start.
We prove that the groups associated with the Revenge Cube and the Professor's Cube can be realized as Galois groups over the rationals.
Following a remark of Lawvere, we explicitly exhibit a particularly elementary bijection between the set T of finite binary trees and the se
Batman... My homology is my cohomology backwards, Batman.........
The well known Joker $\mathcal{A}(1)$-module of Adams and Priddy is known to be realisable as the cohomology of a $1$-connected space. By at
Hot dust-obscured galaxies (hot DOGs) are a rare class of hyperluminous infrared galaxies identified with the Wide-field Infrared Survey Exp
We study admissible subcategories of the bounded derived category of a smooth projective surface that are supported on the exceptional locus
The field of astronomy evolves rapidly, and it is essential to keep up with these changes in order to effectively communicate with the broad
Conway and Doyle have claimed to be able to divide by three. We attempt to replicate their achievement and fail. In the process, we get tang
I show that each etale n-cohomology class on noetherian schemes comes from a Cech cocycle, provided that any n-tuple of points admits an aff
You're telling me a french fried this
Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: fried_rice_joke() takes exactly three arguments (2 given)
Am enthralled by this visualization NASA shared of Artemis II's path through space. The most mathematically accurate little dance. <3
Thinking of you, Earth © NASA Artemis Ⅱ
to all my researchers, students and people in general who love learning: if you don't know this already, i'm about to give you a game changer
connectedpapers
the basic rundown is: you use the search bar to enter a topic, scientific paper name or DOI. the website then offers you a list of papers on the topic, and you choose the one you're looking for/most relevant one. from here, it makes a tree diagram of related papers that are clustered based on topic relatability and colour-coded by time they were produced!
for example: here i search "human B12"
i go ahead and choose the first paper, meaning my graph will be based around it and start from the topics of "b12 levels" and "fraility syndrome"
here is the graph output! you can scroll through all the papers included on the left, and clicking on each one shows you it's position on the chart + will pull up details on the paper on the right hand column (title, authors, citations, abstract/summary and links where the paper can be found)
you get a few free graphs a month before you have to sign up, and i think the free version gives you up to 5 a month. there are paid versions but it really depends how often you need to use this kinda thing.
researchrabbit works similarly. you do need to create an account to use it, but it is completely free (as far as I know), meaning no limits to your collections/graphs.
pokemon image and kernel
birth of venus
this is in excel btw. and this image is exactly half green and half pink. and for each shade of green there is an equal number of "opposite" pink pixels. and this represents a major leap forward in excel macro use by me
the origin of this concept was, oh, what if you were trying to recreate an image as a tapestry? and you had, say, 24 colors of yarn? and you wanted the image to have equal amounts of each color of yarn? how would you effectively use the yarn you had to create the image? you'd have to look at all the colors of the original image, then look at your yarn colors, and find some consistent method for choosing what original colors are replaced with what yarn colors. but then it turns out there's a lot of different rules you could imagine or follow, which produce different-looking images. and you can end up with something like this:
which is cool. and it would be cool to say, find a granny square cardigan pattern with 24 squares, knit these squares, make a sick cardigan. but then i realized i don't know how to knit or anything. and once you accept that there isn't really a clear "application" and this concept lives on a screen, you open yourself up to more possibilities. a la birth of venus.
step 1: python script that looks at the original image and generates an excel spreadsheet the same dimensions (793 x 1322 pixels = 793 x 1322 cells), and each cell is populated with the hex code of the color that appears in that pixel of the original image
step 2: excel macro to generate list of every unique hex code that appears in the excel spreadsheet.
step 3: excel macro to calculate the R, G, B values of each of those hex codes.
step 4: excel macro to fill each cell with the color of that hex code (not necessary, i just like to do it).
step 5: I add in Saturation (the difference between the largest and smallest RGB value) and Lightness (average of all RGB values).
step 6: pick a color palette. i always find myself gravitating towards groovy seventies palettes with warm reds and oranges, so i decided not to do that this time. i looked on coolors and found a color palette that was all dark greens that were similar to each other. there were only like four colors or something in this palette. and to make it truly different from the other project, there should be a small gradient. so i determined the smallest possible change between colors and used an excel macro to color it. i was going to stop here and do the entire image in shades of green (inspired by that guy on tiktok that paints using only one color) but then. idk. i realized the "opposite" of each color was an equally subtly changing pink. so i imagined that the end of this process would be an "abstract" image, with subtle variations of pink and green, that would end up suggesting birth of venus.
so all told, i had 502 unique replacement colors, 251 of which are green, 251 of which are pink. (793 x 1322) / 502 = either 2088 or 2089 of each color.
step 7: find some method for finding the difference between the original colors of the image and my new color palette. I use a method of comparing, R, G, B, S and L:
((abs(R1 - R2) + abs(G1 - G2) + abs(B1 - B2)) / 3) + abs(S1 - S2) + abs(L1 - L2)
and you come up with something like this. on the left, those are colors that appear in the original image. across the top, those greens are the colors i'm replacing it with. in blue, that's the number of each new color i have to work with (it's just blue for contrast). and in the center, this pink area, that's a giant spreadsheet with the "objective" difference between each original color and each replacement color. it's pink because i have some conditional formatting applied, ignore that part.
and in this situation, you have some choices to make. in the original image up there, i used a schema prioritizing light and dark--i.e., i looked at the darkest color (pure black) that appeared in the original image, then found the closest replacement color (i.e., the replacement color with the smallest number). then did the same with the lightest color. then the next darkest, next lightest.
but i'm going to do it slightly differently this time. and i don't know how this image will come out looking.
if you look at the "first" green, closest to the left, and sort by smallest to largest:
you can see that these colors on the left are closest to the "first" green i've decided to work with. that might seem odd. i mean, #7F9800--> #00a94f are pretty close, but #A95400 is red. but that's just a difference in hue. really, #A95400 and #00a94f are very similar in lightness and saturation.
and this also calculates the number of times that color actually appears in the original image. that first specific green, #7F9800, only appears twice. but some colors, like actual black #000000, appear something like 46,000 times. and if you add all the numbers in the "frequency" column, it should exactly equal the sum of each replacement color (2088 ish x 502).
step 8: excel macro again. this one is complicated. basically it sorts that first "green" column (column E in my spreadsheet) from smallest to largest. then it adds each cell in the "frequency" column until it reaches or surpasses the blue cell above column E, which for this particular color is 2089. it copies those "original image" colors and their respective frequencies over to another sheet. for the color that surpassed 2089, it splits in two. then it deletes that column E. Then it makes sure "frequency" and "replacement color sum" still total. then it runs again on the new column E, until the whole spreadsheet is used up. and it generates something like:
[color from original image] [number of times that color appears] [replacement color, filled in]
and there's approximately 8000 lines of that.
i have the replacement colors in the order above. starting with vivid green, slowing transitioning to dark green, switching abruptly to bright pink, slowly transitioning to pale pink.
step 9: another excel macro. this one looks at original image broken down into hex codes, then looks at the generated list and replaces each [original] color with the replacement color, that exact number of times.
end result of these macros, following different "rules" of assigning replacement colors to original colors, is this:
which looks different, obviously. but it is the exact replacement colors, and same number of each replacement color, as the original up there.
at maximum efficiency, it took about 20 minutes to complete step 8 and 9. i have a vision of creating a series of these, each time "starting" with the next replacement color, and then making a gif of it. idk how to make gifs though
@magnetictapedatastorage seems up your alley
With the death of USB-A, we are fast losing our only intuitive physical model of spin-1/2 particles
Here's what I spent the last two days on!
It's a chart of what each chemical element does in the human body, or in that of other organisms
EDIT 27-04-2025: corrected "Fe sulfate" to "Fe sulfide" in the sulfur box and added a note for titanium. See the DeviantArt link for more details.
EDIT 24-05-2025: Thanks to @twoflower-2f, who reminded me that taurine is worth a mention in the sulfur box (see link).
Definition 1.0. Let this be a post.
From Definition 1.0 and the above example of a post it follows that
Lemma 1.1. Some posts are good
Interesting math fact of the day #386:
There is a real number A such that floor(A^(3^n)) is prime for all positive integers n.
what the fuck
