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balavalli - For each of the patterns you are interested in, the probability is high that while you may find a commercial pattern / texture that is close to what you want, it won't be exactly what you want and you will have to modify it. To be honest, for simple patterns, it takes only slightly more time to make your own pattern from scratch than it does to to modify the colors or shapes in an existing pattern, so I would suggest that you learn how to make whatever pattern you need.
Towards this end, here's a short tutorial on how to create many different variants of your pattern #1.
A. Create a single shaded diamond that is as large or larger than you will ever need. I created one ~700px square. The following layer stack screen shot shows how I did this.
01b
I used guides to lay out the diamond shape (ie, square on its side) so it fits perfectly on the canvas and made a selection in this shape. I temporarily made the background color black for good visibility, but I will eventually turn this off to get a transparent background. I used "Color Fill 1", an adjustment layer to set the color of the diamond. I then made selections of (i) the lower two edges, and (ii) the upper two edges, and used these to mask two "Levels" adjustment layers -- one to darken the bottom two edges and one to lighten the upper two edges.
The result is this (with its temporary black background):
01a
The PSD file for this is attached below in zipped form
01c (zipped)
View attachment 01c-shaded_diamonds_seamless_tile_tiling-ps01a_698px_square.zip
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B. I removed the temporary background and shrunk the image down to 200 px on a side, a size suitable for this demo.
02
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C. I defined a pattern based on this using the instructions here:
http://blogs.adobe.com/jkost/2015/01/how-to-create-a-seamless-pattern-tile-in-photoshop.html
Note: because I laid out the diamond perfectly centered within the canvas, I didn't have to use the offset function discussed in the above tutorial.
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D. I opened a new canvas that was the full size needed for the final project. I decided to make it 2000px square.
At the bottom of the layer stack I put a color fill layer. This defines the background color.
Just above this, I put an empty layer, and then used "Edit / Fill / Pattern" to fill this layer with the pattern I defined in step (C), above.
Here is the layer stack that I used:
03a
Layer 1 is the result with a black background,
03c
and Layer 2 is the result with a gray background.
03d
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To get closer to the look in the first example provided by the OP, I also generated a very low contrast version by inserting a "Levels" adjustment layer above Layer 2. The result is:
03e
An almost unlimited number of other variants can be produced from the PSD files just by adjusting parameters such as color, sizes, aspect ratios, brightness, contrast, etc., as well as inserting other adjustment layers or layer styles.
The time it took me to do the actual work was well under 5 minutes. Once you get used to the process it goes extremely fast. You probably spent much more time than this searching for exactly what you want than I did making a very useful template for myself and anyone else that needs a pattern like this. In addition, by learning how to do this yourself, you greatly expand your personal capabilities. Creating seamless tiles is one of the fundamental techniques any decent Photoshop artist really should know.
HTH,
Tom M
PS - I just noticed that the "unit cell", ie, the basic repeating unit in your example #1 is actually 4 slightly differently shaded diamonds, not just one. If you want that level of accuracy in your copy, you just build up to it using 4 slightly different versions of my single diamond adjacent to each other. The basic concept is exactly the same as shown above, just a slight generalization of it.