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Fractal Mandelbrot demo using MemSQL Extensibility
-- First, run this .sql file to load data into the cells table and to create
-- the functions/procedures. Then, you can play around with the demo by
-- SELECTing from the mandelbrot_colors() table valued function. Try
-- running this zsh command for an interesting progression of fractals:
-- zsh -c 'i=3.0; while ((i > 0.0000000001)) && mysql -h 127.0.0.1 -u root -P 3306 --database db <<<"select * from mandelbrot_colors(-0.743643887103515, 0.131825914205310, $i)"; do echo $i; ((i = i /2)); done'
-- You can also pass in a fourth and fifth argument to the mandelobrot_colors function in order to
-- increase the number of pixels.
-- We want 1 byte chars so we can maximize the width of our
-- picture. Group concat has at most 8k bytes, so 1 byte
-- chars and 16 bytes per pixel (of color sequences) gives
-- us a max width of ~500 pixels.
--
set global collation_server = "binary";
set collation_server = "binary";
create database if not exists db;
use db;
create table if not exists cells(r int, c int, primary key rc(r, c));
delimiter //
create or replace procedure fill_cells()
as
declare
_size query(size int) = select count(*) as size from cells;
size int = scalar(_size);
begin
if size = 0 then
for r in 0 .. 1500 loop
insert ignore into cells values (r, 0);
end loop;
insert ignore into cells
select t1.r, t2.r
from cells as t1, cells as t2
where t2.r != 0;
end if;
end //
call fill_cells() //
create or replace function p1(r int, c int)
returns int
as
begin
return r;
end //
create or replace function p2(r int, c int)
returns int
as
begin
return c;
end //
create or replace function complex_double(z record(r double, i double))
returns double
as
begin
return z.r;
end //
create or replace function complex_imaginary(z record(r double, i double))
returns double
as
begin
return z.i;
end //
create or replace function complex_size(c record(r double, i double))
returns double
as
begin
return sqrt(c.r*c.r + c.i*c.i);
end //
create or replace function complex_mult(a record(r double, i double),b record(r double, i double))
returns record(r double, i double)
as
begin
return row(a.r * b.r - a.i * b.i, a.r * b.i + b.r * a.i);
end //
create or replace function complex_add(a record(r double, i double), b record(r double, i double))
returns record(r double, i double)
as
begin
return row(a.r + b.r, a.i + b.i);
end //
create or replace function complex_sub(a record(r double, i double), b record(r double, i double))
returns record(r double, i double)
as
begin
return row(a.r - b.r, a.i - b.i);
end //
create or replace function mandelbrot_dist(c record(r double, i double),
maxiters int default 10000)
returns int
as
declare
z record(r double, i double) not null = row(0, 0);
begin
for i in 1 .. maxiters loop
if complex_size(z) > 2.0 then
return i;
end if;
z = complex_add(complex_mult(z, z), c);
end loop;
return maxiters;
end //
create or replace function mandelbrot_scale(r int, c int, maxr int, maxc int,
cx double, cy double, width double)
returns record(r double, i double)
as
declare
aspect_ratio double = (maxc :> double) / (maxr :> double);
xadjust double = (width/2);
-- Multiply by 2 because most characters are 2x as
-- many pixels high as they are wide.
yadjust double = xadjust / aspect_ratio * 2;
minz record(r double, i double) = row(cx - xadjust, cy - yadjust);
maxz record(r double, i double) = row(cx + xadjust, cy + yadjust);
gap record(r double, i double) = complex_sub(maxz, minz);
begin
return complex_add(minz, row(gap.r * c/maxc, gap.i * (maxr - r - 1)/maxr));
end //
create or replace function bgcolor(color int)
returns mediumtext
as
begin
return CONCAT(UNHEX("1b"), '[48;5;', LPAD(color, 3, "0"), 'm', " ", UNHEX("1b"), '[0m');
end //
create or replace function mandelbrot_char_colors(iters int)
returns mediumtext
as
declare
options array(varchar(24)) =
[17, 4, 18, 19, 20, 21, -- dark blue -> blue
63, 105, 147, 189, 231, 230, 229,
228, 227, 226, 220, 214, 208,
202, 196, 160, 124, 88, 52];
i int = (sqrt(iters * sqrt(iters)) :> int) % length(options);
begin
if iters >= 10000 then
return bgcolor(16);
else
return bgcolor(options[i]);
end if;
end //
create or replace function mandelbrot_char(iters int)
returns varchar(24)
as
declare
options array(varchar(24)) =
[' ', '.', '*', "@", "#"];
i int = (iters / 10000 * (length(options) - 1)) :> int;
begin
return options[i];
end //
create or replace function complex_str(z record(r double, i double))
returns text
as
begin
return LPAD(CONCAT(FORMAT(z.r, 1),
IF(z.i < 0, "", "+"),
FORMAT(z.i, 1), "i"), 10, " ");
end //
create or replace function complex_grid(height int default 6,
width int default 6)
returns table
as return select group_concat(complex_str(mandelbrot_scale(r, c, height, width, -0.5, 0, 3)) separator ", ") as line, rr
from (
select *, rank() over(order by c) rr
from cells
where r < height and c < width
) q1
group by r
order by r
limit height //
create or replace function mandelbrot_dist_grid(height int default 20,
width int default 25)
returns table
as return select group_concat(LPAD(mandelbrot_dist(mandelbrot_scale(r, c, height, width, -0.5, 0, 3), 10), 2, " ") separator ", ") as line, rr
from (
select *, rank() over(order by c) rr
from cells
where r < height and c < width
) q1
group by r
order by r
limit height //
create or replace function mandelbrot(cx double default -0.5,
cy double default 0,
scale double default 3,
height int default 20,
width int default 72)
returns table
as return select group_concat(mandelbrot_char(dist) separator "") as line, rr
from (
select *,
mandelbrot_dist(mandelbrot_scale(r, c, height, width, cx, cy, scale)) as dist,
rank() over(order by c) rr
from cells
where r < height and c < width
) q1
group by r
order by r
limit height //
create or replace function mandelbrot_colors(cx double default -0.5,
cy double default 0,
scale double default 3,
height int default 20,
width int default 72)
returns table
as return select group_concat(mandelbrot_char_colors(dist) separator "") as line, rr
from (
select *, mandelbrot_dist(mandelbrot_scale(r, c, height, width, cx, cy, scale)) as dist, rank() over(order by c) rr
from cells
where r < height and c < width
) q1
group by r
order by r
limit height //
delimiter ;
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