Hexatrigesimal file icon colors

Computer file icon sets are typically for only a limited number of filetypes which often exclude rare or unusual filetypes.  By assigning a 3-digit hexatrigesimal (base-36) number to each filetype, <notranslate>36³ = 46656</notranslate> unique file icons can be generated.

assigning triplets

Begin by assigning every file extension a three-character name.  For most file extensions with more than three characters, the extension can simply be truncated to the first three characters.  Otherwise, new three-character names will need to be assigned to conflating file extensions.  For example: ".xls", ".xlsx", and ".xlsm" can be assigned as "xls", "xlx", and "xlm".

One-letter and two-letter file extensions are represented here as three-letter file extensions by adding trailing zeros: ".m" files are represented as "m00" and ".7z" files are represented as "7z0".

character mapping

Each character from 0 to Z can now be used to represent a hexatrigesimal number digit.  Each hexatrigesimal digit from 0 to Z has to then be assigned an integer decimal (base-10) value from 0 to 255.  This series of decimal integers from 0 to 255 are then converted to their corresponding values of 0 to FF in hexadecimal (base 16).

base-36 number	base-10 number	base-10 value	base-16 value
0	0	0	0
1	1	7	7
2	2	15	F
3	3	22	16
4	4	29	1D
5	5	36	24
6	6	44	2C
7	7	51	33
8	8	58	3A
9	9	66	42
A	10	73	49
B	11	80	50
C	12	87	57
D	13	95	5F
E	14	102	66
F	15	109	6D
G	16	117	75
H	17	124	7C
I	18	131	83
J	19	138	8A
K	20	146	92
L	21	153	99
M	22	160	A0
N	23	168	A8
O	24	175	AF
P	25	182	B6
Q	26	189	BD
R	27	197	C5
S	28	204	CC
T	29	211	D3
U	30	219	DB
V	31	226	E2
W	32	233	E9
X	33	240	F0
Y	34	248	F8
Z	35	255	FF

file extensions

Each 3-character base-36 file extension triplet from "000" to "zzz" now represents one of 36³ = 46656 possible colors from #000000 to #ffffff.

extension	triplet	hexcolor	color
DefaultIcon	000	#000000
7z	7Z0	#33ff00
css	CSS	#57cccc
doc	DOC	#5faf57
docx	DOX	#5faff0
htm	HTM	#7cd3a0
ico	ICO	#8357af
jpg	JPG	#8ab675
mediawiki	MED	#a0665f
mht	MHT	#a07cd3
ods	ODS	#af5fcc
odt	ODT	#af5fd3
oxps	OXP	#aff0b6
pdf	PDF	#b65f6d
png	PNG	#b6a875
svg	SVG	#cce275
txt	TXT	#d3f0d3
xht	XHT	#f07cd3
xls	XLS	#f099cc
xlsx	XLX	#f099f0
xml	XML	#f0a099
xps	XPS	#f0b6cc
zip	ZIP	#ff83b6
^^DIRECTORY^^	ZZZ	#ffffff

problems

There are still a couple of problems here.  The first is that most file extensions do not contain decimal number characters so about ten thousand or thirty percent (~10/36) of available colors are under-utilized.  An attempt to solve this can be by contracting the hexatrigesimal color space from 0₃₆ to Z₃₆ to a hexavigesimal (base-26) color space from A₂₆ to Z₂₆.  This results in 26³ = 17576 possible colors.  But even eliminating 29080 extraneous colors does not help to significantly resolve the second problem in that consecutive colors such as for ".ods" versus ".odt" are extremely difficult to practically impossible to distinguish visually.  Even if the human viewer cannot tell the difference though, the assigned colors are still mathematically unique which provides a second semantic signal to indexing bots in addition to the file extension.  For practical usage by humans, consecutive file extensions are often for the same application.  For example: both ".ods" and ".odt" are for LibreOffice so this still provides a useful semantic cue for the human viewer (as intended) even if these two individual colors cannot be differentiated visually.  There may exist other extension pairs though that could be visually conflated but this problem exists with a traditional icon set as well in that with limited icons available, multiple file extensions have to be assigned the same icon.