From ffa59f06b7ef7d6391d7d373ae041cdcc075353f Mon Sep 17 00:00:00 2001 From: Miloslav Ciz Date: Wed, 20 Jul 2022 18:18:42 +0200 Subject: [PATCH] Update --- anarch.md | 2 +- chess.md | 10 +++++----- collapse.md | 2 +- fail_ab.md | 10 ++++++++++ feminism.md | 5 +++++ how_to.md | 2 +- left_right.md | 2 ++ main.md | 4 ++++ often_confused.md | 4 +++- sdf.md | 2 +- 10 files changed, 33 insertions(+), 10 deletions(-) create mode 100644 fail_ab.md create mode 100644 feminism.md diff --git a/anarch.md b/anarch.md index 97afe97..6962461 100644 --- a/anarch.md +++ b/anarch.md @@ -59,7 +59,7 @@ Gameplay-wise Anarch offers 10 levels and multiple enemy and weapon types. It su ## Technical Details -Anarch's engine uses [raycastlib](raycastlib.md), a LRS library for advanced 1D [ray casting](ray_casting.md) which is often called a "pseudo 3D". This method was used by Wolf3D, but Anarch improves it to allow different levels of floor and ceiling which makes it look a little closer to Doom (which however used a different methods called [BSP](bsp.md) rendering). +Anarch's engine uses [raycastlib](raycastlib.md), a LRS library for advanced 2D [ray casting](ray_casting.md) which is often called a "pseudo 3D". This method was used by Wolf3D, but Anarch improves it to allow different levels of floor and ceiling which makes it look a little closer to Doom (which however used a different methods called [BSP](bsp.md) rendering). The music in the game is [procedurally generated](procedural_generation.md) using [bytebeat](bytebeat.md). diff --git a/chess.md b/chess.md index e348046..2ba6228 100644 --- a/chess.md +++ b/chess.md @@ -32,15 +32,15 @@ During [covid](covid.md) chess has experienced a small boom among normies and [Y {[This](https://www.youtube.com/watch?v=DpXy041BIlA) is an absolutely amazing video about weird chess algorithms :) ~drummyfish} -Chess have a very strong relationship with computers, computers help people play chess, train their skills but also analyze positions, perform research about chess, create and search game databases and find new play styles. The game also provides a nice framework for machine learning. +Chess are a big topic in computer science and programming, computers not only help people play chess, train their skills, analyze positions and perform research of games, but they also allow mathematical analysis of chess and provide a platform for things such as [artificial intelligence](ai.md). There is a great online Wiki focused on programming chess engines: https://www.chessprogramming.org. Chess software is usually separated to **libraries**, **chess engines** and **frontends** (or boards). Chess engine is typically a [CLI](cli.md) program capable of playing chess but also doing other things such as evaluating arbitrary position, hinting best moves, saving and loading games etc. Frontends on the other hand are [GUI](gui.md) programs that help people interact with the underlying engine. -For communication between different engines and frontends there exist standards such as XBoard (engine protocol), UCI (another engine protocol), FEN (way of encoding a position as a string), PGN (way of encoding games as strings) etc. +For communication between different engines and frontends there exist standards such as XBoard (engine [protocol](protocol.md)), UCI (another engine protocol), FEN (way of encoding a position as a string), PGN (way of encoding games as strings) etc. -Computers have already surpassed the best humans in their playing strength (we can't exactly compute an engine's Elo as it depends on hardware used, but generally the strongest would rate high above 3000 FIDE). As of 2021 the strongest chess engine is considered to be the [FOSS](foss.md) engine [Stockfish](stockfish.md), with other strong engines being e.g. Leela Chess Zero (also FOSS) or AlphaZero ([proprietary](proprietary.md), by [Google](google.md)). [GNU Chess](gnu_chess.md) is a reasonably strong [free software](free_software.md) engine by [GNU](gnu.md). There are world championships for chess engines such as the *Top Chess Engine Championship* or *World Computer Chess Championship*. [CCRL](https://ccrl.chessdom.com/ccrl/4040/) is a list of chess engines along with their Elo ratings. Despite the immense strength of modern engines, there are still very specific situation in which humans beat the computer (shown e.g. in [this](https://www.youtube.com/watch?v=R9IZWgArWUE) video). +Computers have already surpassed the best humans in their playing strength (we can't exactly compute an engine's Elo as it depends on hardware used, but generally the strongest would rate high above 3000 FIDE). As of 2021 the strongest chess engine is considered to be the [FOSS](foss.md) engine [Stockfish](stockfish.md), with other strong engines being e.g. Leela Chess Zero (also FOSS) or AlphaZero ([proprietary](proprietary.md), by [Google](google.md)). [GNU Chess](gnu_chess.md) is a pretty strong [free software](free_software.md) engine by [GNU](gnu.md). There are world championships for chess engines such as the *Top Chess Engine Championship* or *World Computer Chess Championship*. [CCRL](https://ccrl.chessdom.com/ccrl/4040/) is a list of chess engines along with their Elo ratings. Despite the immense strength of modern engines, there are still very specific situation in which humans beat the computer (shown e.g. in [this](https://www.youtube.com/watch?v=R9IZWgArWUE) video). The first chess computer that beat the world champion (at the time Gary Kasparov) was famously [Deep Blue](deep_blue.md) in 1997. [Alan Turing](turing.md) himself has written a chess playing algorithm but at his time there were no computers to run it, so he executed it by hand -- nowadays the algorithm has been implemented on computers (there are bots playing this algorithm e.g. on lichess). @@ -48,7 +48,7 @@ For online chess there exist many servers such as https://chess.com or https://c Playing strength is not the only possible measure of chess engine quality, of course -- for example there are people who try to make the **smallest chess programs** (see [countercomplex](countercomplex.md) and [golfing](golf.md)). As of 2022 the leading programmer of smallest chess programs seems to be Óscar Toledo G. (https://nanochess.org/chess.html). Unfortunately his programs are [proprietary](proprietary.md), even though their source code is public. The programs include Toledo Atomchess (392 [x86](x86.md) instructions), Toledo Nanochess (world's smallest [C](c.md) chess program, 1257 non-blank C characters) and Toledo Javascript chess (world's smallest [Javascript](javascript.md) chess program). He won the [IOCCC](ioccc.md). Another small chess program is micro-Max by H. G. Muller (https://home.hccnet.nl/h.g.muller/max-src2.html, 1433 C characters, Toledo claims it is weaker than his program). -{ Nanochess is actually pretty strong, in my testing it easily beat [smallchesslib](smallchesslib.md) :') ~drummyfish } +{ Nanochess is actually pretty strong, in my testing it easily beat [smallchesslib](smallchesslib.md) Q_Q ~drummyfish } ## Variants @@ -74,7 +74,7 @@ Programming chess is a [fun](fun.md) and enriching experience and is therefore r The core of chess programming is writing the [AI](ai.md), everything else, i.e. implementing the rules, communication protocols etc., is pretty straightforward (but still a good programming exercise). Nevertheless one has to pay a great attention to eliminating as many bugs as possible; really, the importance of writing automatic tests can't be stressed enough as debugging the AI will be hard enough and can become unmanageable with small bugs creeping in. -The AI itself works in almost all cases on the same principle: firstly we implement so called static **evaluation function** -- a function that takes a chess position and outputs its evaluation number which say how good the position is for white vs black (positive number favoring white, negative black). This function considers a number of factors such as total material of both players, pawn structure, king safety, piece mobility and so on (in new engines this function is often a learned [neural network](neural_network.md), but it may very well be written by hand). Secondly we implement a **search** algorithm that recursively searches the game tree and looks for a move that will lead to the best result, i.e. to position for which the evaluation function gives the best value. This basic principle, especially the search part, gets very complex as there are many possible weaknesses and optimizations. +The AI itself works in almost all cases on the same principle: firstly we implement so called static **evaluation function** -- a function that takes a chess position and outputs its evaluation number which say how good the position is for white vs black (positive number favoring white, negative black). This function considers a number of factors such as total material of both players, pawn structure, king safety, piece mobility and so on (in new engines this function is often a learned [neural network](neural_network.md), but it may very well be written by hand). Secondly we implement a **search** algorithm -- typically some modification of [minimax](minimax.md) algorithm -- that recursively searches the game tree and looks for a move that will lead to the best result, i.e. to position for which the evaluation function gives the best value. This basic principle, especially the search part, gets very complex as there are many possible weaknesses and optimizations. Exhaustively searching the tree to great depths is not possible due to astronomical numbers of possible move combinations, so the engine has to limit the depth quite greatly. Normally it will search all moves to a small depth (e.g. 2 or 3 half moves or *plys*) and then extend the search for interesting moves such as exchanges or checks. Maybe the greatest danger of searching algorithms is so called **horizon effect** which has to be addressed somehow (e.g. by detecting quiet positions, so called *quiescence*). If not addressed, the horizon effect will make an engine misevaluate certain moves by stopping the evaluation at certain depth even if the played out situation would continue and lead to a vastly different result (imagine e.g. a queen taking a pawn which is guarded by another pawn; if the engine stops evaluating after the pawn take, it will think it's a won pawn, when in fact it's a lost queen). There are also many techniques for reducing the number of searched tree nodes and speeding up the search, for example pruning methods such as **alpha-beta** (which subsequently works best with correctly ordering moves to search), or **transposition tables** (remembering already evaluated position so that they don't have to be evaluated again when encountered by a different path in the tree). diff --git a/collapse.md b/collapse.md index bba9a54..388ce64 100644 --- a/collapse.md +++ b/collapse.md @@ -1,6 +1,6 @@ # Collapse -Collapse of our civilization is something that's very likely coming very soon: we are especially focusing on a very probable **technological collapse** (caused by badly designed technology as well as its wrong application and extreme overuse causing a dangerous dependence) but of course clues point to it coming from many directions (ecological, economical, political, natural disasters such as a coronal mass ejection etc.). Recently there has even appeared a specific term *collapsology* referring to the study of the potential collapse. +Collapse of our civilization is a concerning scenario in which basic structures of society relatively rapidly fall apart and cause world-wide horrors such as chaos, [wars](war.md), famine and loss of advanced technology. It is something that's very likely coming very soon: we are especially focusing on a very probable **technological collapse** (caused by badly designed technology as well as its wrong application and extreme overuse causing a dangerous dependence) but of course clues point to it coming from many directions (ecological, economical, political, natural disasters such as a coronal mass ejection etc.). Recently there has even appeared a specific term *collapsology* referring to the study of the potential collapse. There is a [reddit](reddit.md) community for discussing the collapse at https://reddit.net/r/collapse. [WikiWikiWeb](wikiwikiweb.md) has a related discussion under *ExtinctionOfHumanity*. diff --git a/fail_ab.md b/fail_ab.md new file mode 100644 index 0000000..ab1bd34 --- /dev/null +++ b/fail_ab.md @@ -0,0 +1,10 @@ +# Type A/B Fail + +Type A and type B fails are two very common cases of failing to adhere to the [LRS](lrs.md) politics/philosophy by only a small margin. Most people don't come even close to LRS politically or by their life philosophy -- these are simply general failures. Then there a few who ALMOST adhere to LRS politics and philosophy but fail in an important point, either by being/supporting [pseudoleft](pseudoleft.md) (type A fail) or being/supporting [right](left_right.md) (type B fail). The typical cases are following (specific cases may not fully fit these, of course): + +- **type A fail**: Is anticapitalist, anticonsumerist, supports minimalism, [free software](free_software.md) and [free culture](free_culture.md), may even be a vegan, [anarchist](anarchism.md), [C](c.md) programmer etc., however falls into the trap of supporting [pseudoleft](pseudoleft.md), e.g. LGBT or feminism and things such as censorship ("[moderation](moderation.md)", [COCs](coc.md)), "just violence and bullying" (violence against fascists, e.g. [antifa](antifa.md)), falls for memes such as "[Rust](rust.md) is the new [C](c.md)". +- **type B fail**: Is against [pseudoleft](pseudoleft.md) bullshit and propaganda such as political correctness, is a [racial realist](racial_realism.md), highly supports [suckless](suckless.md) software, hacking and minimalism to achieve high freedom, usually also opposes [corporations](corporation.md) and state, however falls into the trap of being a [fascist](fascism.md), easily accepts violence, believes in "natural selection/wild west as a basis of society", supports and engages in [cryptocurrencies](crypto.md), believes in some form of [capitalism](capitalism.md) and that the current form of it can be "fixed" (["anarcho" capitalism](ancap.md) etc.) + +Type A/B fails are the "great filter" of the rare kind of people who show a great potential for adhering to LRS. It may be due to the modern western culture that forces a [right](right.md)-[pseudoleft](pseudoleft.md) false dichotomy that even those showing a high degree of non-conformance eventually slip into the trap of being caught by one of the two poles. These two fails seem to be a manifestation of an individual's true motives of [self interest](self_interest.md) which is culturally fueled with great force -- those individuals then try to not conform and support non-mainstream concepts like free culture or sucklessness, but eventually only with the goal of self interest. It seems to be extremely difficult to abandon this goal, much more than simply non-conforming. Maybe it's also the subconscious knowledge that adhering completely to LRS means an extreme loneliness; being type A/B fail means being a part of a minority, but still a having a supportive community, not being completely alone. + +However these kinds of people may also pose a hope: if we could educate them and "fix their failure", the LRS community could grow rapidly. If realized, this step could even be seen as the main contribution of LRS -- uniting the misguided rightists and pseudoleftists by pointing out errors in their philosophies (errors that may largely be intentionally forced by the system anyway exactly to create the hostility between the non-conforming, as a means of protecting the system). \ No newline at end of file diff --git a/feminism.md b/feminism.md new file mode 100644 index 0000000..50f3b9c --- /dev/null +++ b/feminism.md @@ -0,0 +1,5 @@ +# Feminism + +Feminism is a [fascist](fascism.md) [terrorist](terrorism.md) [pseudoleftist](pseudoleft.md) movement aiming for establishing female as the superior gender. Similarly to [LGBT](lgbt.md), feminism is hugely violent, [toxic](toxic.md) and harmful, based on [brainwashing](brainwashing.md), [bullying](bullying.md) (e.g. the [metoo](metoo.md) campaign) and [propaganda](propaganda.md). + +If anything's clear, then that feminism doesn't care about gender equality. Firstly it is not called *gender equality movement* but *feminism*, i.e. for-female, and as we know, [name plays a huge role](name_is_important.md). Indeed, women have historically been oppressed and needed support, but once that support reaches equality -- which has basically already happened a long time ago now -- feminist movement will, if only by [social inertia](social_inertia.md), keep pursuing more advantages for women (what else should a movement called *feminism* do?), i.e. at this point the new goal has already become female superiority. Another proof is that feminists care about things such as wage gap but of course absolutely don't give a damn about opposite direction inequality, such as men dying on average much younger than women etc. And of course, when men establish "men rights" movements to address this, suddenly feminists see those as "fascist", "toxic" and "violent" and try to destroy such movements. \ No newline at end of file diff --git a/how_to.md b/how_to.md index 526a0fc..aabced0 100644 --- a/how_to.md +++ b/how_to.md @@ -10,7 +10,7 @@ Firstly let us welcome you, no matter who you are, no matter your political opin If you don't know how to start, here are some basic steps: -1. **Learn about the most essential topics and concepts**, mainly [free software](free_software.md), [open-source](open_source.md), [bloat](bloat.md), [kiss](kiss.md), [capitalist_software](capitalist_software.md), [suckless](suckless.md) and [LRS](lrs.md). +1. **Learn about the most essential topics and concepts**, mainly [free software](free_software.md), [open-source](open_source.md), [bloat](bloat.md), [kiss](kiss.md), [capitalist_software](capitalist_software.md), [suckless](suckless.md), [LRS](lrs.md) and [type A/B fail](fail_ab.md). You will also need to open up your mind and re-learn some toxic concepts you've been taught by the system, e.g. [we do NOT fight anything](fight_culture.md), we do NOT create any [heroes](hero.md) or "leaders" (we follow ideas, not people), [work](work.md) is bad. 2. **Install [GNU](gnu.md)/[Linux](linux.md)** operating system to free yourself from shit like [Windows](windows.md) and [Mac](mac.md) (you can also consider [BSD](bsd.md) but you're probably too noob for that). Do NOT try to switch to "Linux" right away if it's your first time, it's almost impossible, you want to just install "Linux" as [dual boot](dual_boot.md) (alongside your main OS) or on another computer (easier). This way you'll be using both operating systems, slowly getting more comfortable with "Linux" and eventually you'll find yourself uninstalling Windows altogether. You can also just try "Linux" in a [virtual machine](vm.md), from a live CD/flash drive or you can buy something with "Linux" preinstalled like [Raspberry Pi](raspberry.md). **Which "Linux" to install?** There are many options and as a noob you don't have to go hardcore right away, just install any [distro](distro.md) that [just werks](just_werks.md) (don't listen to people who tell you to install [Gentoo](gentoo.md) tho). You can try these: - [Devuan](devuan.md): Nice, [LRS](lrs.md) approved distro that respects your [freedom](free_software.md) that just works, is easy to install and is actually nice. Good for any skill level. - [Debian](debian.md): Like Devuan but uses the evil [systemd](systemd.md) which doesn't have to bother you at this point. Try Debian if Devuan doesn't work for any reason. diff --git a/left_right.md b/left_right.md index ea95099..ae038d4 100644 --- a/left_right.md +++ b/left_right.md @@ -22,6 +22,8 @@ TRUE LEFT (peace, selflessness, forgiveness, ...) We see pseudoleft is something that began as going away from the right but slowly turned around back to its values, just from a slightly different direction. This is because rightism is very easy, it offers tempting short-term solutions such as violence, and so it exhorts a kind of magnetic force on every human -- most cannot resist and only very few get to the true left despite this force. +The current US-centered culture unfortunately forces a **right-pseudoleft false dichotomy**. It is extremely important to realize this dichotomy doesn't hold. Do not become [type A/B fail](fail_ab.md). + What's called *left* in the [modern](modern.md) western culture usually means *pseudoleft*. The existence of pseudoleftism is often overlooked or unknown. It used to be found mainly in the [US](us.md), however globalization spreads this [cancer](cancer.md) all over the world. Pseudoleft justifies its actions with a goal that may seem truly leftist, such as "equality", but uses means completely unacceptable by true left (which are in fact incompatible with equality), such as [violence](violence.md), bullying, lynching, [cancelling](cancel_culture.md), [censorship](censorship.md) or brainwashing. Pseudoleft is aggressive. It believes that **"ends justify the means"** and that **"it's fine to bully a bully"** ("eye for an eye"). A pseudoleftist movement naturally evolves towards shifting its goals from a leftist one such as equality towards a [fascist](fascism.md) one such as a (blind) *fight for some group's rights* (even if that group may already have achieved equality and more). The difference between left and pseudoleft can be shown in many ways; one of them may be that pseudoleft always wants to **[fight](fight_culture.md)** something, usually the right (as they're essentially the same, i.e. natural competitiors). True left wants to end all fights. Pseudoleft invents [bullshit](bullshit.md) artificial issues such as [political correctness](political_correctness.md) that sparks conflict, as it lives by conflict. Left tries to find peace by solving problems. Pseudoleft sees it as acceptable to do bad things to people who commited something it deems bad. True left knows that violence creates violence, it "turns the other cheek", it cures hate with love. diff --git a/main.md b/main.md index 11eeab6..e4801ac 100644 --- a/main.md +++ b/main.md @@ -10,6 +10,8 @@ This is a Wiki for [less retarded software](lrs.md) (LRS) and related topics, ma This wiki is **NOT** a satire. +Are you failure? Learn [which type](fail_ab.md) you are. + { I no longer see any good in this world. This is my last attempt at preserving pure good, however at this point I am alone, it's just for myself in my completely isolated world. Perhaps my love will be shared with a reader far away, in space or time, even if I will never know him. This is the only way I can continue living. I wish you happy reading, my dear friend. ~drummyfish } **Before contributing please read the [rules & style](wiki_style.md)! By contributing you agree to release your contribution under our [waiver](wiki_rights.md).** {But contributions aren't really accepted RN :) ~drummyfish } @@ -37,7 +39,9 @@ If you don't know where to start, here are some suggestions. If you're new, the - [free software](free_software.md) - [suckless](suckless.md) - [less retarded software](lrs.md) +- [anarcho pacifism](anpac.md) - [capitalist software](capitalist_software.md) +- [type A/B fail](fail_ab.md) - [C tutorial](c_tutorial.md) - [pseudoleft](pseudoleft.md) - [history](history.md) diff --git a/often_confused.md b/often_confused.md index a5fc7f1..f231679 100644 --- a/often_confused.md +++ b/often_confused.md @@ -2,7 +2,7 @@ There are many terms that are very similar and are sometimes used interchangeably. This isn't wrong per se, a slight difference may be insignificant in certain contexts. However it's good to know the differences for those cases when they matter. The following list tries to document some of the often confused terms. -- **[AI](ai.md)** vs **[machine learning](machine_learning.md)** +- **[AI](ai.md)** vs **[machine learning](machine_learning.md)** vs **[neural networks](neural_net.md)** - **[algebra](algebra.md)** vs **[arithmetic](arithmetic.md)** - **[algorithm](algorithm.md)** vs **[program](program.md)** - **[analog](analog.md)** vs **[mechanical](mechanical.md)** @@ -11,8 +11,10 @@ There are many terms that are very similar and are sometimes used interchangeabl - **binary** vs **[executable](executable.md)** - **[array](array.md)** vs **[list](list.md)** - **[cepstrum](cepstrum.md)** vs **[spectrum](spectrum.md)** +- **[ASCII art](ascii_art.md)** vs **[ANSI art](ansi_art.md)** - **[assembler](assembler.md)** vs **[assembly](assembly.md)** - **[causation](causation.md)** vs **[correlation](correlation.md)** +- **[demo](demo.md)** vs **[intro](intro.md)** - **[chaos](chaos.md)** vs **[randomness](random.md)** vs **[pseudorandomness](pseudorandom.md)** vs **[entropy](entropy.md)** - **[class](class.md)** vs **[set](set.md)** - **[closed source](closed_source.md)** vs **[proprietary](proprietary.md)** diff --git a/sdf.md b/sdf.md index 25d3ea8..fdbe2f2 100644 --- a/sdf.md +++ b/sdf.md @@ -6,7 +6,7 @@ Sometimes SDF is extended to also return additional information, e.g. the whole **What is it all good for?** We can for example implement quite fast [raytracing](raytracing.md)-like rendering of environments for which we have a fast SDF. While traditional raytracing has to somehow test each ray for potential intersection against all 3D elements in the scene, which can be slow (and complicated), with SDF we can performs so called [raymarching](raymarching.md), i.e. iteratively stepping along the ray according to the distance function (which hints us on how big of a step we can make so that we can potentially quickly jump over big empty areas) until we get close enough to a surface which we interpret as an intersection -- if the SDF is fast, this approach may be pretty efficient ([Godot](godot.md) implemented this algorithm to render real-time global illumination and reflections even in GPUs that don't support accelerated raytracing). Programs for rendering 3D [fractals](fractal.md) (such as Mandelbulber) work on this principle as well. SDFs can also be used as a format for representing shapes such as [fonts](font.md) -- there exists a method (called multi-channel SDF) that stores font glyphs in bitmaps of quite low-resolution that can be rendered at arbitrary scale in a quality almost matching that of the traditional vector font representation -- the advantage over the traditional vector format is obviously greater simplicity and better compatibility with GPU hardware that's optimized for storing and handling bitmaps. Furthermore we can trivially increase or decrease weight (boldness) of a font represented by SDFs simply by adjusting the rendering distance threshold. SDFs can also be used for [collision detection](collision_detection.md) and many other things. One advantage of using SDFs is their **generality** -- if we have an SDF raymarching algorithm, we can plug in any shape and environment just by constructing its SDF, while with traditional raytracing we normally have to write many specialized algorithms for detecting intersections of rays with different kinds of shapes, i.e. we have many special cases to handle. -**How is an SDF implemented?** Well, it's a [function](function.md), it can be implemented however we wish and need, it depends on the use case, but we probably want it to be **fast** because algorithms that work with SDFs commonly call it often. SDF of simple mathematical shapes (and their possible combinations such as unions, see. e.g. [CSG](csg.md)), e.g. spheres, can be implemented very easily (SDF of a sphere = distance to the sphere center minus its radius); even the already mentioned 3D [fractals](fractal.md) have functions that can be used to quickly estimate the distance towards their surface. Other times -- e.g. where arbitrary shapes may appear -- the function may be [precomputed](precomputing.md) into some kind of N dimensional [array](array.md), we might say we use a precomputed [look up table](LUT.md). This can be done in a number of ways, but as a simple example we can imagine raymarching mirror reflections with which we can subdivide the 3D scene into a grid and into each cell we store the SDF value at its center point (which here may be computed by even a relatively slow algorithm), which will allow for relatively fast search of intersections of rays with the surface (at any point along the ray we may check the SDF value of the current cell which will likely provide information for how big a step we can make next). +**How is an SDF implemented?** Well, it's a [function](function.md), it can be implemented however we wish and need, it depends on each case, but we probably want it to be **fast** because algorithms that work with SDFs commonly call it often. SDF of simple mathematical shapes (and their possible combinations such as unions, see. e.g. [CSG](csg.md)), e.g. spheres, can be implemented very easily (SDF of a sphere = distance to the sphere center minus its radius); even the already mentioned 3D [fractals](fractal.md) have functions that can be used to quickly estimate the distance towards their surface. Other times -- e.g. where arbitrary shapes may appear -- the function may be [precomputed](precomputing.md) into some kind of N dimensional [array](array.md), we might say we use a precomputed [look up table](LUT.md). This can be done in a number of ways, but as a simple example we can imagine raymarching mirror reflections with which we can subdivide the 3D scene into a grid and into each cell we store the SDF value at its center point (which here may be computed by even a relatively slow algorithm), which will allow for relatively fast search of intersections of rays with the surface (at any point along the ray we may check the SDF value of the current cell which will likely provide information for how big a step we can make next). ``` . . . . . . . . 3 2 2 2 2 2 2 2