A weird screensaver

Question

As I was gazing at my beautiful Puzzling.SE profile for a while, my screensaver started. But, contrary to what I expected, a completely unknown one appeared. Here is a short GIF of it:

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There are three shapes that appear alternating and move around the screen for a while:

1. A jigsaw puzzling piece (200x280)
2. A StackExchange logo (120x150)
3. An arrow pointing upwards (200x200)

The borders of each of them are outlined with a solid black line, but the inner colors seem to be dependent on the underlying color on the screen at that specific pixel. If you can't view the GIF, here are example images: Jigsaw Piece, StackExchange Logo, Arrow.

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Here are lists of some instances for each shape in the format shapeX,shapeY; pixelX,pixelY; pixelRed,pixelGreen,pixelBlue; convertedPixelRed,convertedPixelGreen,convertedPixelBlue, where the color values range from [0-255] and the used coordinate system is a screen coordinate system (shapeX,shapeY is also the upper left point of the rectangular bounds of each shape).

Jigsaw

988,302; 1129,565; 240,240,240; 240,48,176
627,365; 677,487; 255,255,255; 255,243,219
598,370; 654,510; 111,116,116; 111,228,196
592,371; 783,456; 221,255,255; 221,243,219
545,380; 623,422; 111,116,118; 111,228,14
444,397; 498,520; 255,255,255; 255,243,219
403,405; 472,618; 122,186,168; 122,114,72
403,405; 529,413; 231,232,234; 231,200,210
391,407; 434,649; 114,186,169; 114,114,109
373,410; 448,655; 112,186,170; 112,114,146
196,441; 301,587; 131,186,167; 131,114,35
184,443; 310,701; 100,186,171; 100,114,183
160,447; 181,536; 145,186,165; 145,114,217
143,451; 204,714; 102,189,175; 102,153,75
143,451; 208,587; 131,186,167; 131,114,35
143,451; 230,518; 149,186,164; 149,114,180
137,452; 276,563; 137,186,166; 137,114,254

Logo

118,167; 180,178; 45,46,41; 193,176,137
125,194; 176,303; 210,209,177; 218,232,17
145,268; 247,318; 208,207,178; 112,133,246
151,291; 180,392; 183,186,159; 84,74,90
152,295; 257,405; 180,186,159; 156,190,109
158,318; 170,426; 174,186,160; 168,74,192
162,333; 186,352; 195,194,165; 228,146,190
193,449; 305,532; 146,186,164; 118,190,172
204,488; 301,496; 155,186,163; 241,190,57
219,546; 295,585; 131,186,167; 175,144,71
102,107; 125,123; 246,246,246; 8,230,4
105,119; 126,222; 234,233,197; 120,145,126
110,138; 210,156; 46,47,42; 202,165,222
114,154; 209,200; 240,239,201; 208,229,75
119,173; 145,215; 237,236,199; 92,204,74
147,275; 204,316; 208,207,177; 16,24,17
159,322; 166,338; 199,198,168; 20,54,240
160,326; 174,402; 181,186,159; 188,74,90
218,542; 325,655; 112,186,170; 80,190,94

Arrow

550,440; 636,576; 249,235,225; 25,10,98
580,388; 639,454; 111,116,116; 180,4,45
613,331; 764,417; 154,77,34; 22,78,60
693,192; 798,236; 230,229,193; 58,16,90
695,189; 783,385; 12,13,14; 210,14,5
434,641; 530,766; 99,119,220; 230,55,86
456,603; 463,702; 99,186,172; 170,47,73
530,474; 613,492; 97,115,82; 93,29,45
562,419; 646,475; 111,116,116; 180,4,45
590,370; 669,449; 231,232,234; 220,1,92
608,339; 752,436; 171,235,247; 189,31,97
660,249; 757,435; 212,235,247; 201,14,97
412,679; 481,775; 80,186,175; 174,57,73
484,554; 585,576; 180,184,188; 210,4,74
548,443; 579,541; 64,141,210; 208,70,82
562,419; 680,472; 231,232,234; 220,1,92
616,325; 742,413; 117,188,255; 209,54,100
650,266; 741,386; 12,13,14; 210,14,5
690,197; 821,245; 228,227,191; 58,16,89

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What is the color-changing pattern of each shape and why?

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Hint 1: (arrow shape)

You might find a clue on your keyboard.

Hint 2: (arrow shape)

About me

Answer 1

Jigsaw

The new RGB components depend only on the old ones, individually.
Namely:
$\mathrm{R_{new}} = \mathrm{mod}(1\times\mathrm{R_{old}},256)$
$\mathrm{G_{new}} = \mathrm{mod}(13\times\mathrm{G_{old}},256)$
$\mathrm{B_{new}} = \mathrm{mod}(37\times\mathrm{B_{old}},256)$
The explanation of the factors $1$, $13$ and $37$ might be the number of gold, silver and bronze badges on the profile as shown on the related picture.

Logo

Based on the animation, it seems x coordinates ($\mathrm{pixel}_x-\mathrm{shape}_x$) are important in this one. The logo image is told to be 120x150 pixels, so the thresholds where the rules change are at 40 and 80 pixels on the horizontal axis.
In the left part of it the transformations are:
$\mathrm{R_{new}} = \mathrm{mod}(76\times\mathrm{R_{old}},256)$
$\mathrm{G_{new}} = \mathrm{mod}(105\times\mathrm{G_{old}},256)$
$\mathrm{B_{new}} = \mathrm{mod}(102\times\mathrm{B_{old}},256)$
In the middle:
$\mathrm{R_{new}} = \mathrm{mod}(101\times\mathrm{R_{old}},256)$
$\mathrm{G_{new}} = \mathrm{mod}(104\times\mathrm{G_{old}},256)$
$\mathrm{B_{new}} = \mathrm{mod}(97\times\mathrm{B_{old}},256)$
In the right part:
$\mathrm{R_{new}} = \mathrm{mod}(99\times\mathrm{R_{old}},256)$
$\mathrm{G_{new}} = \mathrm{mod}(107\times\mathrm{G_{old}},256)$
$\mathrm{B_{new}} = \mathrm{mod}(115\times\mathrm{B_{old}},256)$
The numbers in the factors are ASCII code for 'Lifehacks', the name of the hidden community below the logo on the related picture.

Arrow

This seems to be an RGB2HSV conversion (the old RGB channels are converted to HSV, which are interpreted as the new RGB channels - for details of the calculation, see Levieux's answer).
As LukasRotter pointed it out, the 'About me' section on the related picture has only the letters 'H', 'S' and 'B' capitalized, which stand for 'hue', 'saturation' and 'brightness', suggesting an HSB (also called HSV) representation.

Answer 2

Continuing Elias' work on the color changing pattern of the arrow (so please give him credit for it):

$\mathrm{B_{new}} = \mathrm{ROUND}((\mathrm{max}(\mathrm{R_{old}}, \mathrm{R_{old}},\mathrm{R_{old}})/2.55)$ works for all values given by Lukas Rotter. I'm not sure if $2.55$ is indeed the intended value; it is the maximum possible value ($255$) divided by $100$.
For $\mathrm{G_{new}}$ I have:
$\mathrm{G_{new}} = \mathrm{ROUND}((\mathrm{max}(\mathrm{R_{old}}, \mathrm{R_{old}},\mathrm{R_{old}})-\mathrm{min}(\mathrm{R_{old}}, \mathrm{R_{old}},\mathrm{R_{old}}))/(\mathrm{max}(\mathrm{R_{old}}, \mathrm{R_{old}},\mathrm{R_{old}})/100))$
The lay-out is not quite working out as I intended, so I'll explain it a little bit: Take the maximum of the old values, subtract the minimum of the old values and then divide the result by (the same maximum divided by $100$). And finally round the whole thing.
$\mathrm{R_{new}}$ seems to depend (somewhat) on which value out of $\mathrm{R_{old}}$, $\mathrm{G_{old}}$ and $\mathrm{B_{old}}$was the highest.
If $\mathrm{R_{old}}$ has the highest value --> $\mathrm{R_{new}}$ will be low.
if $\mathrm{B_{old}}$ has the highest value --> $\mathrm{R_{new}}$ will be high. Work in progress...
I've also got to work out how this relates to the two hints given...

Update:

As Elias found out the actual conversion is an RGB-to-HSV conversion, where the resulting HSV values are then re-interpreted as RGB values.