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Mandelbrot plot in postgres
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WITH RECURSIVE | |
x(i) AS ( VALUES (0) | |
UNION ALL SELECT i + 1 | |
FROM x | |
WHERE i < 101), | |
Z(Ix, Iy, Cx, Cy, X, Y, I) AS ( | |
SELECT | |
Ix, | |
Iy, | |
X :: FLOAT, | |
Y :: FLOAT, | |
X :: FLOAT, | |
Y :: FLOAT, | |
0 | |
FROM | |
(SELECT | |
-2.2 + 0.031 * i, | |
i | |
FROM x) AS xgen(x, ix) CROSS JOIN | |
(SELECT | |
-1.5 + 0.031 * i, | |
i | |
FROM x) AS ygen(y, iy) | |
UNION ALL | |
SELECT | |
Ix, | |
Iy, | |
Cx, | |
Cy, | |
X * X - Y * Y + Cx AS X, | |
Y * X * 2 + Cy, | |
I + 1 | |
FROM Z | |
WHERE X * X + Y * Y < 16.0 | |
AND I < 27), | |
Zt (Ix, Iy, I) AS ( | |
SELECT | |
Ix, | |
Iy, | |
MAX(I) AS I | |
FROM Z | |
GROUP BY Iy, Ix | |
ORDER BY Iy, Ix | |
) | |
SELECT array_to_string( | |
array_agg(SUBSTRING( | |
' .,,,-----++++%%%%@@@@#### ', GREATEST(I, 1), | |
1 | |
)), '' | |
) | |
FROM Zt | |
GROUP BY Iy | |
ORDER BY Iy; |
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array_to_string | |
-------------------------------------------------------------------------------------------------------- | |
.................................................................................... | |
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....................................................,,,,,,,,,................................. | |
................................................,,,,,,,,,,,,,,,,,,............................. | |
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............................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........................ | |
..........................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...................... | |
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........................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,................... | |
.......................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,................. | |
.......................................,,,,,,,,,,,,,,,,,,,,,,,,--,,,,,,,,,,,,,,,,,,,,................ | |
......................................,,,,,,,,,,,,,,,,,,,,,,,,,,-+--,,,,,,,,,,,,,,,,,,,............... | |
....................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----,,,,,,,,,,,,,,,,,,,.............. | |
...................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,--- -----,,,,,,,,,,,,,,,,,............. | |
.................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---++--++,,,,,,,,,,,,,,,,,,............ | |
................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----%++---,,,,,,,,,,,,,,,,,............ | |
..............................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----+%----,,,,,,,,,,,,,,,,,,........... | |
.............................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,----- %%+----,,,,,,,,,,,,,,,,,,.......... | |
...........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---%-+% ----,,,,,,,,,,,,,,,,,,,......... | |
..........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---+ +## %+%---,,,,,,,,,,,,,,,,,,......... | |
........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----# # +---,,,,,,,,,,,,,,,,,,........ | |
.......................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-------% %-----,,,,,,,,,,,,,,,,,........ | |
.....................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------+ ------,,,,,,,,,,,,,,,,,....... | |
....................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----------+@ +-----------,,,,,,,,,,,,....... | |
..................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,----@-------++ ++-----------,,,,,,,,,,,,...... | |
.................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,--+@% ---+ +@%%@ %%+@+@%------+-,,,,,,,,,,,...... | |
................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---- # ++% % @-----++--,,,,,,,,,,,..... | |
..............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,----+ % %%++ %+%@-,,,,,,,,,,,..... | |
.............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----+# #% ++-,,,,,,,,,,,,.... | |
............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------+ @---,,,,,,,,,,,,.... | |
..........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-------++% ---,,,,,,,,,,,,.... | |
.........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,--------+ + %+---,,,,,,,,,,,,,... | |
........,,,,,,,,,,,,,,,,,,,,,--------------------@ +----,,,,,,,,,,,,... | |
.......,,,,,,,,,,,,,,,,,,,,,,- +-----------------+ ----,,,,,,,,,,,,... | |
.......,,,,,,,,,,,,,,,,,,,,,--++------+---------+% +++--,,,,,,,,,,,,.. | |
......,,,,,,,,,,,,,,,,,,,,,,--%+-----++--------- #+-,,,,,,,,,,,,.. | |
.....,,,,,,,,,,,,,,,,,,,,,,----#%++--+@ -+-----+% --,,,,,,,,,,,,.. | |
.....,,,,,,,,,,,,,,,,,,,,,,-----+## ++@ + +----% +--,,,,,,,,,,,,,.. | |
....,,,,,,,,,,,,,,,,,,,,,,------+@ @ @@++++# +--,,,,,,,,,,,,,.. | |
....,,,,,,,,,,,,,,,,,,,,,-------% #++% -,,,,,,,,,,,,,.. | |
...,,,,,,,,,,,,,,,,,,,,,------++%# %%@ %-,,,,,,,,,,,,,,. | |
...,,,,,,,,,,,,,,,,,,,--------+ % +--,,,,,,,,,,,,,,. | |
...,,,,,,,,,,,,,,,,,,-----+--++@ # --,,,,,,,,,,,,,,. | |
..,,,,,,,,,,,,,,,,,-------%+++% @--,,,,,,,,,,,,,,,. | |
..,,,,,,,,,,,-------------+ @#@ ---,,,,,,,,,,,,,,,. | |
..,,,,,,,,,---@--------@-+% +---,,,,,,,,,,,,,,,. | |
..,,,,,------- +-++++-+%%% +----,,,,,,,,,,,,,,,. | |
..,,,,,,------%--------++% +----,,,,,,,,,,,,,,,. | |
..,,,,,,,,,,--+----------++# ---,,,,,,,,,,,,,,,. | |
..,,,,,,,,,,,,------------+@@@% +--,,,,,,,,,,,,,,,. | |
..,,,,,,,,,,,,,,,,,------- +++% %--,,,,,,,,,,,,,,,. | |
...,,,,,,,,,,,,,,,,,,---------+@ @ --,,,,,,,,,,,,,,. | |
...,,,,,,,,,,,,,,,,,,,,------- # %@ +--,,,,,,,,,,,,,,. | |
...,,,,,,,,,,,,,,,,,,,,,-------++@ %+ %-,,,,,,,,,,,,,,. | |
....,,,,,,,,,,,,,,,,,,,,,------- %++% %-,,,,,,,,,,,,,.. | |
....,,,,,,,,,,,,,,,,,,,,,,------+# %# #@ ++++ +--,,,,,,,,,,,,,.. | |
.....,,,,,,,,,,,,,,,,,,,,,,-----+ %%++% +@+----+ +--,,,,,,,,,,,,,.. | |
.....,,,,,,,,,,,,,,,,,,,,,,,---%+++--+#+--------% #--,,,,,,,,,,,,.. | |
......,,,,,,,,,,,,,,,,,,,,,,--++-----%%--------- @#--,,,,,,,,,,,,.. | |
.......,,,,,,,,,,,,,,,,,,,,,---------------------+@ +-++,,,,,,,,,,,,... | |
........,,,,,,,,,,,,,,,,,,,,,--------------------+ ----,,,,,,,,,,,,... | |
.........,,,,,,,,,,,,,,,,,,,,----,,,------------- #+----,,,,,,,,,,,,... | |
..........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-------+ + +---,,,,,,,,,,,,,... | |
...........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,--------+%# #---,,,,,,,,,,,,.... | |
............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------+# @ @---,,,,,,,,,,,,.... | |
.............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----+# + @--,,,,,,,,,,,,.... | |
..............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---+% %+@ %+-+ +++%-,,,,,,,,,,,..... | |
................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,----% %@++ # % -----++-,,,,,,,,,,,,..... | |
.................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-- ++ ---+ + +%@ %++++++------%-,,,,,,,,,,,...... | |
...................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---- -------++ +------------,,,,,,,,,,,,...... | |
....................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----------+% +--------,,,,,,,,,,,,,,,....... | |
......................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,--------+# -----,,,,,,,,,,,,,,,,,,....... | |
.......................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-------+ #----,,,,,,,,,,,,,,,,,,........ | |
.........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,----+% %#---,,,,,,,,,,,,,,,,,,,........ | |
..........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---+%+%@ %+%%--,,,,,,,,,,,,,,,,,,......... | |
............................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---+-+% %----,,,,,,,,,,,,,,,,,,.......... | |
.............................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----+%@+---,,,,,,,,,,,,,,,,,,,.......... | |
...............................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----+%----,,,,,,,,,,,,,,,,,,........... | |
................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-----%+ +--,,,,,,,,,,,,,,,,,............ | |
..................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---++----,,,,,,,,,,,,,,,,,............. | |
...................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,---@-----,,,,,,,,,,,,,,,,,............. | |
.....................................,,,,,,,,,,,,,,,,,,,,,,,,,,,-----,,,,,,,,,,,,,,,,,,,.............. | |
.....................................,,,,,,,,,,,,,,,,,,,,,,,,,,--%,,,,,,,,,,,,,,,,,,,,............... | |
.......................................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,................. | |
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(102 rows) |
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