Here is an idea for Photoshop. There are a few steps, so I'll just explain the general procedure without going into every detail. Feel free to ask for clarification.
I'll use this image with some random colored blobs as an example:
The red cross is the wanted center.
First we need to make sure that the wanted center is exactly in the center of the image. A ...
Building textures in vector is not easy. Especially if you want the effect to actually be a vector, rather than a pixel effect inside of Illustrator.
A good trick that I use these days is to start in Photoshop and then vectorise in Illustrator.
Create a mid to high resolution image in Photoshop that has the texture you want. You can create this from scratch ...