Simple Drawings with Mathematica | Hacker News Reader

Simple Drawings with Mathematica

leancrew.com

47 pointsingve11 comments

Not a big fan of Python but for simple stuff SAGE Math beats Mathematica ten times over, with the better actual programming language too.

I have yet to find an adequate replacement for Mathematica and its graphics DSL. To create the visualizations in https://math.tali.link/classical-array-algebra/ takes a fair amount of interplay of code and data, I shudder to think how I would do this in a non-term-rewriting language.

    Graphics3D[{Gray, phone, Black, Thick, xaxis, yaxis, zaxis},

This has always seemed an odd API to me, in that the arguments can alternate between "the objects being drawn" and "stylistic configuration params" which act like imperative commands setting the current state of the color or whatnot.

With that said, Wolfram as a whole seems well-designed, so I wonder if I am missing something deeper, and curious to hear the rationale from Wolfram experts.

> which act like imperative commands setting the current state of the color or whatnot

No further insights on the design rationale, but yeah, that's exactly what's going on.

I wouldn't say this is unique to Mathematica e.g. it strongly resembles string streams in C++ or the canvas context in HTML/JS or terminal sequences or many others. They aren't truly arguments in the normal sense, it's a more a single argument which is list of commands where "now draw this shape" is one possibility for a command.

I agree this appears to be the intended mental model.

But if that is the case, I'd expect all the arguments to be of some type like "Command", which is not the case here. These expected objects have types like RGBColor or Cuboid or Circle. So it's a list of heterogenous types, which are interpreted as a series of commands... odd.

Perhaps instead of thinking of this as a function, I should think of it as a mini DSL for constructing graphics.

I'd say it's a bit more involved than a single command stream: you can include any number of nested lists inside the outermost list, and each list acts as its own self-contained scope for configuring the style. For instance, if you write Graphics[{Red, Disk[{-2, 0}], {Green, Disk[{0, 0}]}, Disk[{2, 0}]}], you'll get a green disk surrounded by two red disks. Often, when I'm constructing a long Graphics call, I won't have any commands at all in the top-level list, but instead put each part in an isolated sublist.

Nice question, to which I do not know the answer.

Note that Graphics[...] is also used to 'internally' define any internal graphical object, as you can see with InputForm[Plot[...]]. And the chosen syntax seems particularly easy to parse (so as to generate a bitmap, say). So maybe it was designed primarily with that in mind rather than as an API?

According to the documentation Graphics[] has been a part of Mathematica since v1 from 1988. It is probably one of the functions that did not exist in Mathematica's predecessors (like SMP [1]) which largely focused on symbolic algebra. So it might have been up to Wolfram himself to invent a convenient syntax from scratch.

[1] See https://writings.stephenwolfram.com/2013/06/there-was-a-time... but, in typical Wolfram style, insufficient credit seems to be given to other symbolic manipulation products that existed at the time.

I used Mathematica a lot in my PhD. I never really understood this syntax, using a second layer of braces to separate the primitives would have made more sense to me. Many other parts of the Wolfram language I found to be intuitive and well designed.

Consider a set of symbols where all of the symbols in the set can be described in terms of other symbols in the set.

There's a name for that in the world of shape-grammar type things but I forget what it is.

I think that any such "self describing" set would lend itself to being translated to other self describing sets. It might even be guaranteed. A neat transform.

A software language could be like that.

We could do a subset of math that is like that.

It's eminently feasible to do a drawing system like that.

I don't know if there's any direct relation but this reminds me of:

http://conal.net/talks/denotational-design-lambdajam-2015.pd...

https://www.youtube.com/watch?v=bmKYiUOEo2A

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