Array-programming the Mandelbrot set(jcmorrow.com)
jcmorrow.com
Array-programming the Mandelbrot set
https://jcmorrow.com/mandelbrot/
22 comments
Mega-cool. This is a totally different way to think about it. Uiua seems intimidating, I had never heard of it before.
You should definitely check out uiua (https://www.uiua.org/)! Array programming can certainly be intimidating, but I think it's worth doing for a few reasons:
- The "array"-ish solution to a problem is usually a very data-oriented solution. Even if you aren't working in an array-oriented language (and just to be clear, I'm not advocating that people write production code in array languages), "thinking in arrays" helps me come up with more elegant solutions.
- Learning array programming is a little like learning to program all over again. If you really enjoyed the process of learning to program, it lights up those same brain circuits, which I found really enjoyable.
- If you ever want to do any graphics programming the mental model can be very helpful. Array programming really helped me wrap my mind around how shader programs are executed.
Uiua is little unique in that it is also a stack-based language, so learning both paradigms at the same time can definitely be a little challenging, but I think it's well worth it.
- The "array"-ish solution to a problem is usually a very data-oriented solution. Even if you aren't working in an array-oriented language (and just to be clear, I'm not advocating that people write production code in array languages), "thinking in arrays" helps me come up with more elegant solutions.
- Learning array programming is a little like learning to program all over again. If you really enjoyed the process of learning to program, it lights up those same brain circuits, which I found really enjoyable.
- If you ever want to do any graphics programming the mental model can be very helpful. Array programming really helped me wrap my mind around how shader programs are executed.
Uiua is little unique in that it is also a stack-based language, so learning both paradigms at the same time can definitely be a little challenging, but I think it's well worth it.
Uiua is super friendly. Like the friendliest language ever. It breaks your brain for sure, but in a pleasant way.
It is by far the easiest way to learn an array based language; thanks largely to the web based “Pad” and the clever text to symbol way of writing the code. Do some of the tutorial stuff, it’s fun and all inline on the web. Works great on mobile! Think of it like sudoku, but for programming. You can do real stuff with it also, but for me it’s just for fun.
It is by far the easiest way to learn an array based language; thanks largely to the web based “Pad” and the clever text to symbol way of writing the code. Do some of the tutorial stuff, it’s fun and all inline on the web. Works great on mobile! Think of it like sudoku, but for programming. You can do real stuff with it also, but for me it’s just for fun.
Just started going through the tutorial, and it is, indeed, mega-cool.
Btw, here's the identity matrix of size 3:
˙⊞=⇡3
(It takes the range [0,1,2] then outerproducts it with itself through equality.)
Btw, here's the identity matrix of size 3:
˙⊞=⇡3
(It takes the range [0,1,2] then outerproducts it with itself through equality.)
Is Uiua really pronounced the way it says so on the site ? It feels wrong.
Haha, I think I understand what you mean, but also, how else would you say uiua? I was at a total loss when I first read it.
I asked Google to describe it and it described how I pronounce it:
"Uiua" is pronounced like "oo-ee-oo-ah", with the sounds flowing together. The "u" sound is like in "boo," and the "i" sound is like in "see," while the final "ua" is a combination of the "oo" sound and the "ah" sound.
"Uiua" is pronounced like "oo-ee-oo-ah", with the sounds flowing together. The "u" sound is like in "boo," and the "i" sound is like in "see," while the final "ua" is a combination of the "oo" sound and the "ah" sound.
> As is often the case with array programming, I revisited this last week only to realize I couldn’t read it
> The advantage of array languages in my experience has always been their immediacy.
They seem to have a lot in common with regexes in that regard. Super useful for interactive use cases in editors, search engines, etc. But if you find yourself saving a regex it's at least code smell and probably a red flag.
Some of the array language people seem to think it's sane to write an entire program in regex-lang, which is less red flag and more red banner flying through the sky.
> The advantage of array languages in my experience has always been their immediacy.
They seem to have a lot in common with regexes in that regard. Super useful for interactive use cases in editors, search engines, etc. But if you find yourself saving a regex it's at least code smell and probably a red flag.
Some of the array language people seem to think it's sane to write an entire program in regex-lang, which is less red flag and more red banner flying through the sky.
The author is clearly a novice who has just tinkered with array languages a little. Extrapolating from that to absolute properties of a tool seem a bit overeager, don't you think? For example, do you think you could design a legible analog circuit without significant time learning the craft?
My experience is with APL, but I think it is capable of producing some of the most readable and maintainable codebases out there. I've worked for years in various projects using Python, Java, C, Scheme, and a smattering of many other languages. However, it's really hard to overstate the clarity that comes from data-oriented design and dogged elimination of API boundaries.
It just takes a long time to learn to write good software in good APL style. In many ways all the in vogue best practices these days around declarative and functional programming tend to work antithetically to writing good array code. This means that the learning curve for experienced programmers is, perhaps paradoxically, higher than that of a totally naive beginning coder.
I really wish I knew some way to directly convey the experience of working with APL at a high level. There's really nothing else much like it.
My experience is with APL, but I think it is capable of producing some of the most readable and maintainable codebases out there. I've worked for years in various projects using Python, Java, C, Scheme, and a smattering of many other languages. However, it's really hard to overstate the clarity that comes from data-oriented design and dogged elimination of API boundaries.
It just takes a long time to learn to write good software in good APL style. In many ways all the in vogue best practices these days around declarative and functional programming tend to work antithetically to writing good array code. This means that the learning curve for experienced programmers is, perhaps paradoxically, higher than that of a totally naive beginning coder.
I really wish I knew some way to directly convey the experience of working with APL at a high level. There's really nothing else much like it.
> My experience is with APL, but I think it is capable of producing some of the most readable and maintainable codebases out there.
Cool! Do you have any public examples to point to? I would be curious to see how a larger project looks, given that I only use array languages for side projects, so my code is often not very legible (e.g. https://github.com/jcmorrow/advent_of_code/blob/master/day_2...).
Cool! Do you have any public examples to point to? I would be curious to see how a larger project looks, given that I only use array languages for side projects, so my code is often not very legible (e.g. https://github.com/jcmorrow/advent_of_code/blob/master/day_2...).
My YAML loader[0] is a condensed example of the architecture and techniques I'm thinking of. It's a couple years old, so the code is dirty by my current standards, but the couple of times I've gone back to read it, I have found the YAML-specific concerns to be quite salient.
That said, it's specifically written for an audience that is familiar with YAML detail in particular, parsing more generally, and of course APL expressions of ideas. In fact, that is a big part of what makes the code readable and maintainable: it is optimized for communicating to the expert worker not for on-boarding new developers. The latter is more appropriately handled via other means IMHO.
The poster child for this style of APL is Co-dfns[0]. It's a production APL compiler and a much larger example of the code I'm talking about. The entrypoint to read is cmp/PS.apl.
If you're interested, I'm willing to have a chat and talk more about what makes this kind of APL imminently workable, in which case there are also some personal private examples I could share as well. Feel free to reach out to the contact info on my profile here.
[0]:https://github.com/xelxebar/dayaml/blob/master/Y.apln.
[1]:https://github.com/Co-dfns/Co-dfns
That said, it's specifically written for an audience that is familiar with YAML detail in particular, parsing more generally, and of course APL expressions of ideas. In fact, that is a big part of what makes the code readable and maintainable: it is optimized for communicating to the expert worker not for on-boarding new developers. The latter is more appropriately handled via other means IMHO.
The poster child for this style of APL is Co-dfns[0]. It's a production APL compiler and a much larger example of the code I'm talking about. The entrypoint to read is cmp/PS.apl.
If you're interested, I'm willing to have a chat and talk more about what makes this kind of APL imminently workable, in which case there are also some personal private examples I could share as well. Feel free to reach out to the contact info on my profile here.
[0]:https://github.com/xelxebar/dayaml/blob/master/Y.apln.
[1]:https://github.com/Co-dfns/Co-dfns
You won't get anything from vapourware salesmen.
It seemingly takes a long time to write good software too, co-dfns is infinity+1 years in progress...
100% agree. Even when I am working with J or Uiua enough that I can comfortably read them, I can't really imagine trying to work on a large (even just thousands of lines, let alone larger) project in them. I know that they exist, and I assume that with a team of competent programmers some different mechanisms would evolve to make things easier to understand, but given the choice between Java and uiua, I would much rather maintain a multi-person multi-year project in Java. The verbosity/boilerplate becomes a strength in that setting, rather than a weakness.
I have experience working with large codebases in K. In practice, most of those codebases don't look dramatically different from any other garden-variety dynamic language. The high-level architectures are similar, and intrinsically-serial business logic still tends to have a lot of named function calls and conditionals. The algorithmic parts, where real work is happening, shrink down to little clusters of operators here and there. Prototypes of new systems and services can be written in a terse, brick-of-code style like some of the K you may find online, but as they get integrated into larger systems they tend to grow comments, descriptive identifier names, and shorter, more diff-friendly lines.
I've never found it hard to come back to reading K after long absences, in no small part because the set of primitives in K is a small fraction of the set in J (or uiua) and the notation, while terse, is more suggestive and legible to me than J's emphasis on digraphs and forks, or the "unicode-soup" of mismatched characters that some modern APL descendants reach for. K is an equally excellent notation for experimenting in a REPL or discussing ideas on a whiteboard.
I've never found it hard to come back to reading K after long absences, in no small part because the set of primitives in K is a small fraction of the set in J (or uiua) and the notation, while terse, is more suggestive and legible to me than J's emphasis on digraphs and forks, or the "unicode-soup" of mismatched characters that some modern APL descendants reach for. K is an equally excellent notation for experimenting in a REPL or discussing ideas on a whiteboard.
Thanks for sharing that perspective! I have not delved too far into k, though I have been a few times confused and discouraged by the fact that there are different versions of the language that are not compatible with each other, and some are proprietary (if I understand the state of the language correctly). Is there a specific version that is best to learn first?
Edit: I just realized that you are the creator of https://beyondloom.com/tools/specialk.html and https://beyondloom.com/decker/index.html. I just want to say that your work is awesome! I've really enjoyed reading through your website many a time.
Edit: I just realized that you are the creator of https://beyondloom.com/tools/specialk.html and https://beyondloom.com/decker/index.html. I just want to say that your work is awesome! I've really enjoyed reading through your website many a time.
ngn/k is a performant FOSS implementation of k6, but it has many constraints and limitations that may make composing large programs difficult. It may be the best dialect for tinkering and learning the language. https://codeberg.org/ngn/k
oK is a slow browser-based FOSS implementation of k6, with fun bells and whistles like "iKe", a visual livecoding environment. ngn/k and oK have diverged a bit, but are largely similar: https://github.com/JohnEarnest/ok
Q is a K-derived language built into kdb+; this is probably the most commercially viable dialect to learn, with the best educational materials (I recommend Nick Psaris' Q Tips), but it is proprietary, with (last I checked) free licenses available for personal use.
If you've seen Decker you may also have been exposed to Lil, which is similar in many ways to Q. It is more verbose and less expressive than Q or K, but I've generally heard people say they find it comparatively accessible: http://beyondloom.com/tools/trylil.html
oK is a slow browser-based FOSS implementation of k6, with fun bells and whistles like "iKe", a visual livecoding environment. ngn/k and oK have diverged a bit, but are largely similar: https://github.com/JohnEarnest/ok
Q is a K-derived language built into kdb+; this is probably the most commercially viable dialect to learn, with the best educational materials (I recommend Nick Psaris' Q Tips), but it is proprietary, with (last I checked) free licenses available for personal use.
If you've seen Decker you may also have been exposed to Lil, which is similar in many ways to Q. It is more verbose and less expressive than Q or K, but I've generally heard people say they find it comparatively accessible: http://beyondloom.com/tools/trylil.html
I think this often boils down to the same criticisms directed to LISP's FORMAT? https://gigamonkeys.com/book/a-few-format-recipes has my favorite take, "While FORMAT's control strings can be cryptic, at least a single FORMAT expression doesn't clutter things up too badly."
Feels like the same would be true for the array languages. Obviously code golfing it all down to be an array manipulation is going to be unreadable. But if you are legit doing manipulations on an array of data, probably going to be pretty hairy in the expanded version, as well. I can see wins from not necessarily naming every intermediate part of the process.
Feels like the same would be true for the array languages. Obviously code golfing it all down to be an array manipulation is going to be unreadable. But if you are legit doing manipulations on an array of data, probably going to be pretty hairy in the expanded version, as well. I can see wins from not necessarily naming every intermediate part of the process.
I see "R" being used multiple times in the expression
seems like it wasn't array-combinator codegolfed enough
seems like it wasn't array-combinator codegolfed enough
I know that you are joking, but in fact I have further golfed it down to reduce the repetition : )
it's the only pattern I saw in array language videos - you guys keep golfing until everything is used only once, even though combinators become impossible to untangle
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