/etc/ImageMagick/thresholds.xml is in imagemagick-common 8:6.6.9.7-5ubuntu3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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<!DOCTYPE thresholds [
<!ELEMENT thresholds (threshold)+>
<!ELEMENT threshold (description , levels)>
<!ELEMENT description (CDATA)>
<!ELEMENT levels (CDATA)>
<!ATTLIST threshold map ID #REQUIRED>
<!ATTLIST levels width CDATA #REQUIRED>
<!ATTLIST levels height CDATA #REQUIRED>
<!ATTLIST levels divisor CDATA #REQUIRED>
]>
<!--
Threshold Maps for Ordered Posterized Dither
Each "<threshold>" element defines the map name, description, and an array
of "levels" used to provide the threshold map for ordered dithering and
digital halftoning.
The "alias" attribute provides a backward compatible name for this threshold
map (pre-dating IM v6.2.9-6), and are deprecated.
The description is a english description of what the threshold map achieves
and is only used for 'listing' the maps.
The map itself is a rectangular array of integers or threshold "levels"
of the given "width" and "height" declared within the enclosing <levels>
element. That is "width*height" integers or "levels" *must* be provided
within each map.
Each of the "levels" integer values (each value representing the threshold
intensity "level/divisor" at which that pixel is turned on. The "levels"
integers given can be any postive integers between "0" and the "divisor",
excluding those limits.
The "divisor" not only defines the upper limit and threshold divisor for each
"level" but also the total number of pseudo-levels the threshold mapping
creates and fills with a dither pattern. That is a ordered bitmap dither
of a pure greyscale gradient will use a maximum of "divisor" ordered bitmap
patterns, including the patterns with all the pixels 'on' and all the pixel
'off'. It may define less patterns than that, but the color channels will
be thresholded in units based on "divisor".
Alternatively for a multi-level posterization, ImageMagick inserts
"divisor-2" dither patterns (as defined by the threshold map) between each of
channel color level produced.
For example the map "o2x2" has a divisor of 5, which will define 3 bitmap
patterns plus the patterns with all pixels 'on' and 'off'. A greyscale
gradient will thus have 5 distinct areas.
-->
<thresholds>
<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Minimal Dither and Non-Dither Threshold Maps
-->
<threshold map="threshold" alias="1x1">
<description>Threshold 1x1 (non-dither)</description>
<levels width="1" height="1" divisor="2">
1
</levels>
</threshold>
<threshold map="checks" alias="2x1">
<description>Checkerboard 2x1 (dither)</description>
<levels width="2" height="2" divisor="3">
1 2
2 1
</levels>
</threshold>
<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
(dispersed) Ordered Dither Patterns
-->
<threshold map="o2x2" alias="2x2">
<description>Ordered 2x2 (dispersed)</description>
<levels width="2" height="2" divisor="5">
1 3
4 2
</levels>
</threshold>
<threshold map="o3x3" alias="3x3">
<description>Ordered 3x3 (dispersed)</description>
<levels width="3" height="3" divisor="10">
3 7 4
6 1 9
2 8 5
</levels>
</threshold>
<threshold map="o4x4" alias="4x4">
<!--
From "Dithering Algorithms"
http://www.efg2.com/Lab/Library/ImageProcessing/DHALF.TXT
-->
<description>Ordered 4x4 (dispersed)</description>
<levels width="4" height="4" divisor="17">
1 9 3 11
13 5 15 7
4 12 2 10
16 8 14 6
</levels>
</threshold>
<threshold map="o8x8" alias="8x8">
<!-- Extracted from original 'OrderedDither()' Function -->
<description>Ordered 8x8 (dispersed)</description>
<levels width="8" height="8" divisor="65">
1 49 13 61 4 52 16 64
33 17 45 29 36 20 48 32
9 57 5 53 12 60 8 56
41 25 37 21 44 28 40 24
3 51 15 63 2 50 14 62
35 19 47 31 34 18 46 30
11 59 7 55 10 58 6 54
43 27 39 23 42 26 38 22
</levels>
</threshold>
<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Halftones - Angled 45 degrees
Initially added to ImageMagick by Glenn Randers-Pehrson, IM v6.2.8-6,
modified to be more symmetrical with intensity by Anthony, IM v6.2.9-7
These patterns initially start as circles, but then form diamonds
pattern at the 50% threshold level, before forming negated circles,
as it approached the other threshold extereme.
-->
<threshold map="h4x4a" alias="4x1">
<description>Halftone 4x4 (angled)</description>
<levels width="4" height="4" divisor="9">
4 2 7 5
3 1 8 6
7 5 4 2
8 6 3 1
</levels>
</threshold>
<threshold map="h6x6a" alias="6x1">
<description>Halftone 6x6 (angled)</description>
<levels width="6" height="6" divisor="19">
14 13 10 8 2 3
16 18 12 7 1 4
15 17 11 9 6 5
8 2 3 14 13 10
7 1 4 16 18 12
9 6 5 15 17 11
</levels>
</threshold>
<threshold map="h8x8a" alias="8x1">
<description>Halftone 8x8 (angled)</description>
<levels width="8" height="8" divisor="33">
13 7 8 14 17 21 22 18
6 1 3 9 28 31 29 23
5 2 4 10 27 32 30 24
16 12 11 15 20 26 25 19
17 21 22 18 13 7 8 14
28 31 29 23 6 1 3 9
27 32 30 24 5 2 4 10
20 26 25 19 16 12 11 15
</levels>
</threshold>
<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Halftones - Orthogonally Aligned, or Un-angled
Initially added by Anthony Thyssen, IM v6.2.9-5 using techniques from
"Dithering & Halftoning" by Gernot Haffmann
http://www.fho-emden.de/~hoffmann/hilb010101.pdf
These patterns initially start as circles, but then form square
pattern at the 50% threshold level, before forming negated circles,
as it approached the other threshold extereme.
-->
<threshold map="h4x4o">
<description>Halftone 4x4 (orthogonal)</description>
<levels width="4" height="4" divisor="17">
7 13 11 4
12 16 14 8
10 15 6 2
5 9 3 1
</levels>
</threshold>
<threshold map="h6x6o">
<description>Halftone 6x6 (orthogonal)</description>
<levels width="6" height="6" divisor="37">
7 17 27 14 9 4
21 29 33 31 18 11
24 32 36 34 25 22
19 30 35 28 20 10
8 15 26 16 6 2
5 13 23 12 3 1
</levels>
</threshold>
<threshold map="h8x8o">
<description>Halftone 8x8 (orthogonal)</description>
<levels width="8" height="8" divisor="65">
7 21 33 43 36 19 9 4
16 27 51 55 49 29 14 11
31 47 57 61 59 45 35 23
41 53 60 64 62 52 40 38
37 44 58 63 56 46 30 22
15 28 48 54 50 26 17 10
8 18 34 42 32 20 6 2
5 13 25 39 24 12 3 1
</levels>
</threshold>
<threshold map="h16x16o">
<!--
Direct extract from "Dithering & Halftoning" by Gernot Haffmann.
This may need some fine tuning for symmetry of the halftone dots,
as it was a mathematically formulated pattern.
-->
<description>Halftone 16x16 (orthogonal)</description>
<levels width="16" height="16" divisor="257">
4 12 24 44 72 100 136 152 150 134 98 70 42 23 11 3
7 16 32 52 76 104 144 160 158 142 102 74 50 31 15 6
19 27 40 60 92 132 168 180 178 166 130 90 58 39 26 18
36 48 56 80 124 176 188 204 203 187 175 122 79 55 47 35
64 68 84 116 164 200 212 224 223 211 199 162 114 83 67 63
88 96 112 156 192 216 232 240 239 231 214 190 154 111 95 87
108 120 148 184 208 228 244 252 251 243 226 206 182 147 119 107
128 140 172 196 219 235 247 256 255 246 234 218 194 171 139 127
126 138 170 195 220 236 248 253 254 245 233 217 193 169 137 125
106 118 146 183 207 227 242 249 250 241 225 205 181 145 117 105
86 94 110 155 191 215 229 238 237 230 213 189 153 109 93 85
62 66 82 115 163 198 210 221 222 209 197 161 113 81 65 61
34 46 54 78 123 174 186 202 201 185 173 121 77 53 45 33
20 28 37 59 91 131 167 179 177 165 129 89 57 38 25 17
8 13 29 51 75 103 143 159 157 141 101 73 49 30 14 5
1 9 21 43 71 99 135 151 149 133 97 69 41 22 10 2
</levels>
</threshold>
<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Halftones - Orthogonally Expanding Circle Patterns
Added by Glenn Randers-Pehrson, 4 Nov 2010, ImageMagick 6.6.5-6
Rather than producing a diamond 50% threshold pattern, these
continue to generate larger (overlapping) circles. They are
more like a true halftone pattern formed by covering a surface
with either pure white or pure black circular dots.
WARNING: true halftone patterns only use true circles even in
areas of highly varying intensity. Threshold dither patterns
can generate distorted circles in such areas.
-->
<threshold map="c5x5b" alias="c5x5">
<description>Circles 5x5 (black)</description>
<levels width="5" height="5" divisor="26">
1 21 16 15 4
5 17 20 19 14
6 21 25 24 12
7 18 22 23 11
2 8 9 10 3
</levels>
</threshold>
<threshold map="c5x5w">
<description>Circles 5x5 (white)</description>
<levels width="5" height="5" divisor="26">
25 21 10 11 22
20 9 6 7 12
19 5 1 2 13
18 8 4 3 14
24 17 16 15 23
</levels>
</threshold>
<threshold map="c6x6b" alias="c6x6">
<description>Circles 6x6 (black)</description>
<levels width="6" height="6" divisor="37">
1 5 14 13 12 4
6 22 28 27 21 11
15 29 35 34 26 20
16 30 36 33 25 19
7 23 31 32 24 10
2 8 17 18 9 3
</levels>
</threshold>
<threshold map="c6x6w">
<description>Circles 6x6 (white)</description>
<levels width="6" height="6" divisor="37">
36 32 23 24 25 33
31 15 9 10 16 26
22 8 2 3 11 17
21 7 1 4 12 18
30 14 6 5 13 27
35 29 20 19 28 34
</levels>
</threshold>
<threshold map="c7x7b" alias="c7x7">
<description>Circles 7x7 (black)</description>
<levels width="7" height="7" divisor="50">
3 9 18 28 17 8 2
10 24 33 39 32 23 7
19 34 44 48 43 31 16
25 40 45 49 47 38 27
20 35 41 46 42 29 15
11 21 36 37 28 22 6
4 12 13 26 14 5 1
</levels>
</threshold>
<threshold map="c7x7w">
<description>Circles 7x7 (white)</description>
<levels width="7" height="7" divisor="50">
47 41 32 22 33 42 48
40 26 17 11 18 27 43
31 16 6 2 7 19 34
25 10 5 1 3 12 23
30 15 9 4 8 20 35
39 29 14 13 21 28 44
46 38 37 24 36 45 49
</levels>
</threshold>
<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Special Purpose Dithers
-->
</thresholds>
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