Great! Thanks!

As someone with 200+ apple trees in my 7 acre yard, this is fun to think about. My trees are planted in rows, which is practical if a bit boring.

But there are certain pragmatic constraints involved in planting apple trees.

The orchardist needs access to the trees from two sides both for maintenance (pruning, spraying, etc.) and also to harvest apples. Assuming semi-dwarf trees, this involves aisles with a minimum width of about 22 ft (ca. 6.7 m) starting from the center of each trunk. The trees should be planted no closer than intervals of 16 ft (ca. 4.9 m) to give them enough air and light.

So how big does an orchard need to be for each of these configurations? Eyeballing it, only configurations in which there is a small variation in the segments connecting trees could realistically be planted as something that would, on the ground, resemble an orchard. Most of the configurations would require an enormous amount of land and so are mostly mathematical abstractions rather than something one could really implement.

How can we modify this to accommodate real trees? The simplest way might be to treat it as packing problem involving circles 8 ft. in diameter that also need 6 ft. of breathing space on two sides.

One advantage I see in the configurations with a small variation in segment length is that planting the orchard to look like a simple mandala reduces the amount of grass under the trees to be maintained, thus significantly reducing mowing and therefore labor and gasoline costs. So it is not completely foolish to consider planting at least a small orchard this way. I am somewhat attracted to the 25 tree pentagon configuration because of its center empty circle, creating a private grove space. Taking into account an air gap around the outside, my guess is that a circle in the field of about 125 ft in diameter should be big enough. That center circle could, for example, hold a very nice circle of wildflowers 20 ft. across for bee forage, maybe some bee hives in the center, and still leave room for equipment to navigate. Another advantage: this would be a good layout for planting five types of trees in groups of five. The could then be easily identified in their mini-groves and harvested together.

So what would the Wolfram Language code be that would tell me how much land I needed and the placement of the trees? (I might actually try this.)

A further thought: if one were considering using the pentagon configuration, one might also want to consider the Orchard Visibility Problem.