Data Update

Task/Julia-set/Transact-SQL/julia-set.sql

@@ -0,0 +1,113 @@
+-- Juila Set
+-- SQL Server 2017 and above
+SET NOCOUNT ON
+GO
+
+-- Plot area 800 X 600
+DECLARE @width INT = 800
+DECLARE @height INT = 600
+
+DECLARE @r_min DECIMAL (10, 8) = -1.5;
+DECLARE @r_max DECIMAL (10, 8) = 1.5;
+DECLARE @i_min DECIMAL (10, 8) = -1;
+DECLARE @i_max DECIMAL (10, 8) = 1;
+
+DECLARE @zoom INT = 1,
+		@moveX INT = 0,
+		@moveY INT = 0;
+
+DECLARE @iter INT = 255; -- Iteration
+
+DROP TABLE IF EXISTS dbo.Numbers
+DROP TABLE IF EXISTS dbo.julia_set;
+
+CREATE TABLE dbo.Numbers (n INT);
+
+-- Generate a number table of 1000 rows
+;WITH N1(n) AS
+(
+    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL
+    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL
+    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1
+), -- 10
+N2(n) AS (SELECT 1 FROM N1 CROSS JOIN N1 AS b), -- 10*10
+N3(n) AS (SELECT 1 FROM N1 CROSS JOIN N2) -- 10*100
+INSERT INTO dbo.Numbers (n)
+SELECT n = ROW_NUMBER() OVER (ORDER BY n)
+FROM N3 ORDER BY n;
+/*
+-- If the version is SQL Server 2022 and above
+INSERT INTO dbo.Numbers (n)
+SELECT value FROM GENERATE_SERIES(0, 1000);
+*/
+
+CREATE TABLE dbo.julia_set
+(
+	a INT,
+	b INT,
+	c_re DECIMAL (10, 8),
+	c_im DECIMAL (10, 8),
+	z_re DECIMAL (10, 8) DEFAULT 0,
+	z_im DECIMAL (10, 8) DEFAULT 0,
+	znew_re DECIMAL (10, 8) DEFAULT 0,
+	znew_im DECIMAL (10, 8) DEFAULT 0,
+	steps INT DEFAULT 0,
+	active BIT DEFAULT 1,
+)
+
+-- Store all the z_re, z_im with constant c_re, c_im corresponding to each point in the plot area
+-- Generate 480,000 rows (800 X 600)
+INSERT INTO dbo.julia_set (a, b, c_re, c_im, z_re, z_im, steps)
+SELECT   a.n as a, b.n as b
+		,-0.7 AS c_re
+		,0.27015 AS c_im
+		,@r_max * (a.n - @width / 2) / (0.5 * @zoom * @width) + @moveX AS z_re
+		,@i_max * (b.n - @height / 2) / (0.5 * @zoom * @height) + @moveY AS z_im
+		,@iter as steps
+FROM
+		(
+		SELECT n - 1 as n FROM dbo.Numbers WHERE n <= @width
+		) as a
+CROSS JOIN
+		(
+		SELECT n - 1 as n FROM dbo.Numbers WHERE n <= @height
+		) as b;
+
+-- Iteration
+WHILE (@iter > 1)
+	BEGIN
+
+		UPDATE dbo.julia_set
+		SET
+			znew_re = POWER(z_re,2)-POWER(z_im,2)+c_re,
+			znew_im = 2*z_re*z_im+c_im,
+			steps = steps-1
+		WHERE active=1;
+
+		UPDATE dbo.julia_set
+		SET
+			z_re=znew_re,
+			z_im=znew_im,
+			active= CASE
+						WHEN POWER(znew_re,2)+POWER(znew_im,2)>4 THEN 0
+						ELSE 1
+					END
+		WHERE active=1;
+
+		SET @iter = @iter - 1;
+	END
+
+-- Generating PPM File
+-- Save the below query results to a file with extension .ppm
+-- NOTE : All the unwanted info like 'rows affected', 'completed time' etc. needs to be
+-- removed from the file. Most of the image editing softwares and online viewers can display the .ppm file
+SELECT 'P3' UNION ALL
+SELECT CAST(@width AS VARCHAR(5)) + ' ' + CAST(@height AS VARCHAR(5)) UNION ALL
+SELECT '255' UNION ALL
+SELECT
+	STRING_AGG(CAST(CASE WHEN active = 1 THEN 0 ELSE 55 + steps % 200 END AS VARCHAR(MAX)) + ' ' -- R
+	+ CAST(CASE WHEN active = 1 THEN 0 ELSE 55+POWER(steps,3) %  200 END AS VARCHAR(MAX)) + ' '  -- G
+	+ CAST(CASE WHEN active = 1 THEN 0 ELSE 55+ POWER(steps,2) % 200 END AS VARCHAR(MAX))		-- B
+	, ' ') WITHIN GROUP (ORDER BY a, b)
+FROM dbo.julia_set
+GROUP BY a, b