No, it is much more complicated than a LUT, but its a black box.
i am sure it is not just LUT and curves but still it probably is quite simple computationally wise.
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What makes you say that?
Because the processing power on cameras is quite limited, but i might be wrong.
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Yes, but the processor is tuned for image processing, it doesnāt use the same type of processor as your computer.
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Itās weird because Iāve never been a huge fan of Fujiās colours (and Iām a long-time Fuji shooter). Iām certainly in the minority, though; some people consider them sublime (I know Iām not colour blind, so maybe I just donāt have a soul 
).
Do you mean colour rendition in general or specific film simulations? Because thereās a world of difference between all the different film simulations with regard to colour. I find Velvia too gaudy, but I love Classic Neg for itās combination of warm and cold tones, for example.
If you mean colour rendition in general, then I would probably say youāre in the minority, yes, because colour is one of the most praised aspects of Fujiās ecosystem. But your opinion is the only thing thatās important to you and your enjoyment of photography. What do you shoot?
The colour rendition in general.
Maybe I just canāt appreciate how good they are because Iāve never used anything different? Maybe, if someone gave me a different camera, Iād be saying āOh my good Aunt Betty! These colours are awful! Gimme my Fuji back!ā
Maybe I just canāt see it until itās pointed out? Maybe itās just not so important to me? (I shoot street and documentary photography). No idea. Maybe (and most likely) Iām just plain weird.
I must admit Iām not sure what people are referring to when they say the āFuji coloursā, because all raw files from every manufacturer are dull and not very colourful. So, they must be talking about the JPEGs, and then you have to talk about film simulations because every JPEG from a Fuji camera uses one. The default Provia is perhaps the truest representation of the Fuji colour look, but from my experience in Fuji communities, the favourite film sims are the ones like Classic Chrome, which give that old school cool film look.
For what itās worth, I used to shoot Canon before getting a Fuji camera, and when I process my old Canon files, I notice a difference in the colours and how I have to decrease the red in the Canon files to get a more pleasing and accurate look. I donāt have to do this with my Fuji files. But Iām not sure that really constitutes anything valuable in terms of colour rendition 
So, youāre not weird at all!
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Same here, colors from canon raw were always too red / magenta. Fuji raw seems more neutral.
But the Fuji jpeg Magic is very helpful - at least for me - if I want to create a consistent look for a bigger series of images. Something I could never recreate from raw images.
My reply is not very productive, but fuji film simulations are very complicated and I donāt think one can recreate them easily.
Have a read here to get an idea of their inner working: https://www.imaging-resource.com/news/2020/08/18/fujifilm-film-simulations-definitive-guide
I donāt think we can recreate these simulations as a simple lut table.
That said, Iām a total amateur so take this with a grain of salt! You already have several good answers here.
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Since Fujifilm themselves publish film simulation LUTs for their log video files, I think itās safe to say that they can indeed be implemented as LUTs. Also note that Capture One and Lightroom and DxO, the three biggest commercial applications in raw editing, use (what amounts to) LUTs in their software to implement Fuji Film Simulations.
And lest we forget, Fuji implemented film simulations on the original X-Pro1, a woefully underpowered camera that surely didnāt have the processing power for some elaborate physical simulation.
Their marketing department has done a amazing job at creating a mystique around these fabled Film Simulations. In reality, they are fancy names for image presets like theyāre available in any other camera. (And to be frank, donāt look particularly like analog Provia or Astia much at all). Still, they provide a nice look, and are maybe more thoughtfully designed than others. I very much like them and use them every day.
But at least to the limit of my understanding, they do not contain any magic pixie dust.
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there is also the free capture one express fuji version, that has some presets which are supposed to be the fuji ones, named the same etc, I donāt think theyāre as nice as the in-camera ones, mostly from that software I use the āfilm high contrastā preset, it is the only program I have at the moment which will read the x-t5 lossy compressed rawās
this is c1ās āeternaā preset with some edits to the colours, they have a simplified interface which I like, where you can choose, red, orange etc then tweak hue, saturation, and lightness
Thatās an interesting perspective to hear. I did feel that there is more to it than simple presets, but again my experience with other Cameras is quite limited. Thanks.
Well, Iād say the Film Simulations are special in that they strive not for correctness, but for a pleasing, film-like look. There are quite drastic hue distortions in some of them, which arenāt really realistic, but do lead to a beautiful image. This is what Fuji themselves call āmemory colorā, as opposed to realistic color.
And of course you have the choice between varying degrees of realism, with Provia being relatively neutral, and e.g. Velvia or Nostalgic Neg going into a more artistic direction.
Most other manufacturers instead strive for merely varying contrasts and saturations in their picture profiles, but leave hue alone for the most part. Notable exceptions are e.g. Ricohās Positive/Negative Film modes, and Olympus had a few cool ones as well. And in their own communities, these are similarly revered as Fujiās Film Simulations. (I personally like Ricohās Negative Film particularly, not unlike Classic Chrome with warm shadows and a soft, desaturated Highlight rolloff).
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In my personal tests I was never able to fully recreate the ooc results by using luts. At least not for video which is where I have the matching luts for.
So, my assumption is that the jpeg engine does something additional than just applying a lut.
Maybe someone has a more detailed insight to this topic?
one feature I read says thats the case, that itās not just luts, another one said itās luts, whatever it is the processing seems instant, whereas my panasonics take some seconds to create a new jpeg from a raw
The newer cameras have a ācolor chromeā and āclarityā effect, IIRC. These sound like spacial algorithms, which a LUT can not replicate. I have not experimented with these, yet, though, so I canāt say much more about them. Another possible gotcha could be the white balance implementation. If thereās some sort of adaptive CAT involved, it might be nonlinear, too.
in capture 1 the clarity is like a diffuse and sharpen slider, the fuji menus have an explainer, I think the color chrome is extra colour in the shadows or something
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Yeah, and if the clarity slider is used, JPEGās are no longer instant and do take a few seconds more, at least on the X100V. Afaik color chrome and chrome blue fx darken specific colors in the highlights.