I'm trying to find an filter/texture I can use to make the same effect. Am currently using Adobe Illustrator and GIMP.
Thanks in advance!
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Since you mentioned GIMP, here's a simple method
Fill a bacgkround layer with the colour you want
Create a new white layer, and apply the noise filter. Set the layer mode to Multiply
Create a new transparent layer. Choose the Chalk 02 brush, set to a large size, increase the Spacing in the Tool options. Then paint to create a random texture, lower the layer opacity as required.
I think it will be difficult for you to find a filter or effect that will reproduce this in one click. It looks to me like your sample image has several different texture overlays applied to it- one that lightens the base color and one that darkens the base color in places.
I suggest that if you are really into this then try some of your own and come back if you have any particular questions or difficulties.
There are many ways to "make textures". Often, textures like this are made with overlaying vector or raster texture files onto a base artwork (which can be as simple as a filled rectangle). Vector textures will contain a very large quantity of anchor points and can result in very large file sizes. So depending on your intended output and unless you need a lot of scalability I would suggest using raster overlays.
I am not familiar with Gimp but I believe it has similar properties to Photoshop. These texture overlays work equally well in Photoshop or Illustrator. Obviously, if used in a Vector application the resulting files will not be totally Vector. I tend to use raster texture overlays in Illustrator with no problems. There are many Vector and Raster texture files available on the web (probably even some that are free). I like to make my own photographs of texture surfaces which I find and then manipulate them in Photoshop.
You can use black and white, or black and transparent, or even color textures from photos and then apply a combination of blend modes and opacity settings to dial in the desired look.
The example below was made in Illustrator with raster overlays and has a base color rectangle:
This is the texture file I am using:
Here is the first texture applied with a Blend Mode of Luminosity at 8% Opacity:
And here is the same texture rotated 90 degrees and applied again- with Blend Mode Overlay at 14% Opacity:
I would be remiss if I did not give kudos to Von Glitschka and his wonderful use of textures in his work and his sharing of some of his techniques for this- if you are into learning more about this he is an excellent person to look into (no affiliation).