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0 The Whothm Drawing Language
1 ===========================
2
3 _Try it online_ [@ catseye.tc](https://catseye.tc/installation/Whothm)
4 | _See also:_ [Etcha](https://github.com/catseye/Etcha)
5
6 - - - -
7
8 Overview
9 --------
10
11 Whothm is a language for describing infinite two-colour bitmapped
12 graphics.
13
14 ### Prerequisites
15
16 I'd love to tell you about Whothm, but first I need to tell you about
17 Joanie, the Gnostic Babysitter. Have you seen her? She's a very normal
18 twelve-year-old girl, with very normal twelve-year-old girl concerns —
19 she worries if her friends will make fun of her for liking different
20 music than they do, worries if that cute boy in home room likes her or
21 not, worries if she'll be able to achieve a transcendant state of gnosis
22 at the moment of her physical death so that her soul may be freed from
23 the reincarnation cycle. Because, you see, she's a Gnostic. Not just
24 curious about Gnosticism, not just going through a phase, or anything
25 like that — Joanie is a die-hard, demiurge-rejecting,
26 rotten-material-world-shunning Gnostic. And she charges $15 an hour.
27
28 OK, *now* I can tell you about Whothm.
29
30 ### Program Structure
31
32 Each Whothm program consists of a variable declaration section and a
33 single infinite loop.
34
35 There are two possible data types for variables: rectangles and truth
36 tables. A rectangle is a structure of four integer members called x, y,
37 w and h. A truth table is a map from pairs of boolean values to a single
38 boolean value. A truth table is denoted by listing only the pairs which
39 evaluate to true; all other pairs evaluate to false.
40
41 Inside the infinite loop, there are two kinds of commands: draw commands
42 and delta commands. Draw commands apply a rectangle to the drawing
43 canvas. Every pixel on the canvas that lies within w pixels to the right
44 of the x position, and within h pixels to the bottom of the y position,
45 is changed. A truth table is given that determines how it is changed.
46 The existing pixel is looked up in the first column of the table, and
47 the pixel in the rectangle being drawn (which is always true) is looked
48 up in the second column; the resulting pixel state is read off the third
49 column. Truth maps to the foreground colour (typically black), while
50 falsehood maps to the background colour (typically white.)
51
52 Delta commands alter a named member of a named rectangle. They always
53 add a value to the member, although that value may be negative. The
54 value may be a literal constant, or it may be the current value of a
55 named member of a named rectangle.
56
57 Syntax
58 ------
59
60 ### Grammar
61
62 Whothm ::= {Declaration ";"} "begin" {Command ";"} "end".
63 Declaration ::= Name<new> ":=" (RectDecl | TableDecl).
64 RectDecl ::= "(" IntLit "," IntLit "," IntLit "," IntLit ")".
65 TableDecl ::= TruthPair {"/" TruthPair}.
66 TruthPair ::= "TT" | "TF" | "FT" | "FF".
67 Command ::= DrawCmd | DeltaCmd.
68 DrawCmd ::= "draw" Name<Rect> "," Name<Table>.
69 DeltaCmd ::= MemberRef "+=" (IntLit | MemberRef).
70 MemberRef ::= Name<Rect> "." RectMember.
71 RectMember ::= "x" | "y" | "w" | "h".
72
73 ### Example Program
74
75 r := (0, 0, 1, 2);
76
77 AND := TT;
78 OR := TT/TF/FT;
79 NAND := TF/FT/FF;
80 NOR := FF;
81 XOR := TF/FT;
82
83 begin
84 r.x += 5;
85 r.y += r.w;
86 draw r, XOR;
87 end
88
89 Semantics
90 ---------
91
92 The meaning of a Whothm program is fairly intuitive. The commands
93 between the `begin` and `end` are executed in sequence, altering the
94 state of the drawing canvas, and of one or more rectangles. (There is no
95 way to alter a truth table, once defined.) The whole sequence of
96 commands is then repeated, *ad infinitum*.
97
98 However, note that Whothm is a language for describing only shapes which
99 are (countably) infinte in extent. For this reason, it is an error for
100 the state of the program (that is, the variables and the canvas) to be
101 the same on any two (even non-consecutive) iterations of the loop.
102
103 Discussion
104 ----------
105
106 Whothm raises some interesting questions, although not perhaps as
107 interesting as those raised by Joanie's grades this semester. The main
108 one is, what kinds of shapes can Whothm describe?
109
110 Clearly, the shapes cannot be chaotic in any strong sense, as the
111 equations involved are essentially linear. The sole exception is when a
112 truth tables like XOR, which can reverse previous pixels, is used. In
113 fact, the presence of XOR means that Whothm can generate infinite
114 drawings without a fixed point. (XOR seems a bit like sine in that
115 respect; you can't take the indefinite integral of it, because never
116 ever settles down.) Yet, I believe it is not necessary — any shape that
117 can be drawn with XOR can be drawn with suitable monotonic truth tables,
118 as well.
119
120 Further, despite not being able to produce clearly chaotic drawings,
121 Whothm can still produce what are in my opinion somewhat pretty ones.
122
123 Cat's Eye Technologies' implementation of Whothm is called JWhothm, as
124 it is written in Java. Using a browser which supports Java applets, it
125 can be interacted with in the [JWhothm
126 exhibit](http://catseye.tc/gallery/esolangs/jwhothm/) in the [Gallery of
127 Interactive Esolangs](http://catseye.tc/gallery/esolangs/).
128
129 _(Update 2023: Cat's Eye Technologies now has another implementation of_
130 _Whothm, called [whothm.lua](impl/whothm.lua/), and_ it is this that is_
131 _now [installed online at catseye.tc](https://catseye.tc/installation/Whothm),_
132 _replacing the now-defunct "JWhothm exhibit" linked to above.)_
133
134 Happy infinite drawing!
135 Chris Pressey
136 June 29, 2010
137 Evanston, IL
138 Birthplace of Donald Rumsfeld... and Grace Slick
0 The Whothm Drawing Language
1 ===========================
2
3 _Try it online_ [@ catseye.tc](https://catseye.tc/installation/Whothm)
4 | _See also:_ [Etcha](https://github.com/catseye/Etcha)
5
6 - - - -
7
8 Overview
9 --------
10
11 Whothm is a language for describing infinite two-colour bitmapped
12 graphics.
13
14 ### Prerequisites
15
16 I'd love to tell you about Whothm, but first I need to tell you about
17 Joanie, the Gnostic Babysitter. Have you seen her? She's a very normal
18 twelve-year-old girl, with very normal twelve-year-old girl concerns —
19 she worries if her friends will make fun of her for liking different
20 music than they do, worries if that cute boy in home room likes her or
21 not, worries if she'll be able to achieve a transcendant state of gnosis
22 at the moment of her physical death so that her soul may be freed from
23 the reincarnation cycle. Because, you see, she's a Gnostic. Not just
24 curious about Gnosticism, not just going through a phase, or anything
25 like that — Joanie is a die-hard, demiurge-rejecting,
26 rotten-material-world-shunning Gnostic. And she charges $15 an hour.
27
28 OK, *now* I can tell you about Whothm.
29
30 ### Program Structure
31
32 Each Whothm program consists of a variable declaration section and a
33 single infinite loop.
34
35 There are two possible data types for variables: rectangles and truth
36 tables. A rectangle is a structure of four integer members called x, y,
37 w and h. A truth table is a map from pairs of boolean values to a single
38 boolean value. A truth table is denoted by listing only the pairs which
39 evaluate to true; all other pairs evaluate to false.
40
41 Inside the infinite loop, there are two kinds of commands: draw commands
42 and delta commands. Draw commands apply a rectangle to the drawing
43 canvas. Every pixel on the canvas that lies within w pixels to the right
44 of the x position, and within h pixels to the bottom of the y position,
45 is changed. A truth table is given that determines how it is changed.
46 The existing pixel is looked up in the first column of the table, and
47 the pixel in the rectangle being drawn (which is always true) is looked
48 up in the second column; the resulting pixel state is read off the third
49 column. Truth maps to the foreground colour (typically black), while
50 falsehood maps to the background colour (typically white.)
51
52 Delta commands alter a named member of a named rectangle. They always
53 add a value to the member, although that value may be negative. The
54 value may be a literal constant, or it may be the current value of a
55 named member of a named rectangle.
56
57 Syntax
58 ------
59
60 ### Grammar
61
62 Whothm ::= {Declaration ";"} "begin" {Command ";"} "end".
63 Declaration ::= Name<new> ":=" (RectDecl | TableDecl).
64 RectDecl ::= "(" IntLit "," IntLit "," IntLit "," IntLit ")".
65 TableDecl ::= TruthPair {"/" TruthPair}.
66 TruthPair ::= "TT" | "TF" | "FT" | "FF".
67 Command ::= DrawCmd | DeltaCmd.
68 DrawCmd ::= "draw" Name<Rect> "," Name<Table>.
69 DeltaCmd ::= MemberRef "+=" (IntLit | MemberRef).
70 MemberRef ::= Name<Rect> "." RectMember.
71 RectMember ::= "x" | "y" | "w" | "h".
72
73 ### Example Program
74
75 r := (0, 0, 1, 2);
76
77 AND := TT;
78 OR := TT/TF/FT;
79 NAND := TF/FT/FF;
80 NOR := FF;
81 XOR := TF/FT;
82
83 begin
84 r.x += 5;
85 r.y += r.w;
86 draw r, XOR;
87 end
88
89 Semantics
90 ---------
91
92 The meaning of a Whothm program is fairly intuitive. The commands
93 between the `begin` and `end` are executed in sequence, altering the
94 state of the drawing canvas, and of one or more rectangles. (There is no
95 way to alter a truth table, once defined.) The whole sequence of
96 commands is then repeated, *ad infinitum*.
97
98 However, note that Whothm is a language for describing only shapes which
99 are (countably) infinte in extent. For this reason, it is an error for
100 the state of the program (that is, the variables and the canvas) to be
101 the same on any two (even non-consecutive) iterations of the loop.
102
103 Discussion
104 ----------
105
106 Whothm raises some interesting questions, although not perhaps as
107 interesting as those raised by Joanie's grades this semester. The main
108 one is, what kinds of shapes can Whothm describe?
109
110 Clearly, the shapes cannot be chaotic in any strong sense, as the
111 equations involved are essentially linear. The sole exception is when a
112 truth tables like XOR, which can reverse previous pixels, is used. In
113 fact, the presence of XOR means that Whothm can generate infinite
114 drawings without a fixed point. (XOR seems a bit like sine in that
115 respect; you can't take the indefinite integral of it, because never
116 ever settles down.) Yet, I believe it is not necessary — any shape that
117 can be drawn with XOR can be drawn with suitable monotonic truth tables,
118 as well.
119
120 Further, despite not being able to produce clearly chaotic drawings,
121 Whothm can still produce what are in my opinion somewhat pretty ones.
122
123 Cat's Eye Technologies' implementation of Whothm is called JWhothm, as
124 it is written in Java. Using a browser which supports Java applets, it
125 can be interacted with in the [JWhothm
126 exhibit](http://catseye.tc/gallery/esolangs/jwhothm/) in the [Gallery of
127 Interactive Esolangs](http://catseye.tc/gallery/esolangs/).
128
129 _(Update 2023: Cat's Eye Technologies now has another implementation of_
130 _Whothm, called [whothm.lua](impl/whothm.lua/), and_ it is this that is_
131 _now [installed online at catseye.tc](https://catseye.tc/installation/Whothm),_
132 _replacing the now-defunct "JWhothm exhibit" linked to above.)_
133
134 Happy infinite drawing!
135 Chris Pressey
136 June 29, 2010
137 Evanston, IL
138 Birthplace of Donald Rumsfeld... and Grace Slick