This is a great observation. You have spotted a style of paving that relies heavily on the skill of the installer rather than the repetitive manufacturing of the paver itself.
To answer your questions directly: No, there is no repeating mathematical or geometric pattern here.
The style you are looking at is commonly known as "Crazy Paving," "Flagstone Paving" (specifically irregular flagstone), or "Random Polygonal Paving."
It looks laborious because it is more labor-intensive than laying square bricks, but it does not require hand-crafting every single tile from raw stock.
Here is a breakdown of how this random arrangement is achieved practically and efficiently.
1. The Material Arrives pre-"Broken"
The most crucial part of the puzzle is the source material. The masons are not buying large square slabs and cutting crazy shapes out of them.
When you order this type of natural stone (it looks like sandstone or perhaps a slate variety in your image), it arrives on pallets as large, irregular, quarried slabs of varying sizes. They are already in random polygonal shapes straight from the quarry.
2. The "Giant Jigsaw Puzzle" Method
The installation process is essentially solving a giant jigsaw puzzle that has no picture and pieces that weren't originally designed to fit together.
Here is the typical workflow for a professional mason:
Sorting: The masons will usually sort the stone on the grass nearby, separating very large "hero" pieces from medium pieces and smaller filler pieces.
Placement Strategy: They start by laying the largest, most attractive slabs first, spacing them out randomly along the path.
Finding the Fit: They then look at the gaps created between the large slabs. They will go to their sorted piles and hunt for a medium-sized piece whose natural edge roughly matches the curve or angle of the gap they are trying to fill.
The "Rule of Three": A sign of good crazy paving is that generally, no more than three stones should meet at any one joint. If four corners meet, it creates an ugly "cross" that draws the eye and ruins the random illusion. The masons in your image have done this very well.
3. The "Cheat": On-Site Trimming
You mentioned the worry about "labouriously hand-crafting" every tile. While they try to use the natural shapes as much as possible, they do cut the stone.
However, they aren't cutting the whole shape. They are "trimming to fit."
If a mason finds a piece that fits perfectly on two sides but has a sharp corner sticking out on the third side that blocks the next piece, they will use a diamond-blade angle grinder or a masonry saw to quickly lop off that offending corner.
They only cut what they have to in order to make the puzzle pieces snug.
Summary
The "pattern" you see is not designed beforehand; it is emergent. It arises from the mason making hundreds of small decisions on-site about which rock fits best next to the previous one, combined with minor trimming to tighten the joints.
It is a testament to skilled labor. A poor mason will leave wide, ugly mortar joints because they can't be bothered to find the right pieces or trim them. A skilled mason, like the one who did the path in your image, achieves tight, consistent joints that make the path look cohesive despite the randomness of the shapes.
