To shift the texture randomly on different objects, the easiest way is to change its location along any of the axes by a random value.
There is a convenient opportunity in the Cycles render engine to render an object with shadows on a transparent background using material with the “shadow catcher” option. There is no such material in EEVEE render engine, however, in EEVEE we can make our own “shadow catcher” based only on nodes.
The simplest way to pixelate texture, procedural or not – get the color from the single pixel and fill the region with required width and height (resolution) with this color.
Here is the gradient texture with red – green – blue colors:
To pixelate it with the first step of resolution we can make some vectors manipulations.
Creating separate elements of procedural textures in Blender is quite simply – find the desired formula, rebuilt it using mathematical nodes, and as a result, get the desired shape. However, textures created this way have one feature – no tiling. Tiling – a cyclic texture duplication, most time is considered harmful, and professional 3D artists try to avoid texture tiling. But sometimes tiling is necessary, for example, when creating patterns or ornaments.
The procedural texture element is always created in a single instance. This is because all the mathematics that forms the actual procedural image is based on the initial data – coordinates that start from 0, spread out to infinity and not repeat. However, the same mathematics helps us to solve this problem.