Improving Global Landscapes

Looking at the mixed landscape from the previous post

there are a few problems that would be nice to address. The first is that substituting in a child limit set creates a distribution of patches (good) but each patch is solidly that one limit set, which looks a bit extreme. Here I show a simple case of substituting the green tree-tree set on the top sphere:

bottom image is the generating spheres with an arrow showing the substitution.

We can get rid of that solidity by making the child limit set substitute back to the parent. In this case the same sphere is substituting back:

I prefer this way of viewing the substitutions, even if it could sometimes be ambiguous:

You can substitute a different sphere back to get a less geometric result:

but I'm not sure if the surface is continuous in this case. You have to be careful with overlapping spheres when making substitutions.

If the tree area is now too sparse you can substitute back to the golden sphere limit set only on a grandchild instead:

barely noticeable from this distance but there are little patches of 'smooth earth' inside the green areas here.

The second problem is that the patches are perfectly round. In fact deeper zooms would be less round patches as that is partially due to the outer set being perfectly icosahedral. But they'd still be fairly round. 

One way to fix this is to substitute multiple overlapping spheres across to the child set rather than lone spheres. The first step would be two overlapping spheres.  

The only way I know how to do this currently is for those two spheres and neighbours to be the same (up to a Mobius transformation) in the child limit set. That reduces the free spheres to adjust to four. But due to the lack of symmetry it only allows one parameter to change. So back to tree-tree / shell-shell structures.

If we make a brown such tree-tree on sphere 0:

then we can also add one to sphere 1, since we made the child set match 0,1 and their neighbours:

this is continuoue and invariant to order of sphere processing. If we make sphere 0's sphere 0 substitute to child sphere 0 and sphere 1's sphere 1 substitute to child sphere 1 then we get smaller surface patches. They are round in some places, but at the overlap (top left) they combine correctly into longer shapes, which wouldn't otherwise happen. We usually have problems when substituting neighbouring spheres: 

The third problem is that we can't do substitutions on neighbouring spheres. But we can use the same solution above, just give the child sets different values of the shell-shell to tree-tree parameter. 

Here sphere 0 links to the brown tree-tree set and sphere 1 links to the grey shell-shell:

Notice that the overlap between top and left patches prioritises sphere 0 (top). That means sphere processing order does effect the shape. The only fix to this would be to create some sort of tree/shell mixture in the overlap and I currently don't know how to do this.

Nevertheless, the landscape still works in the sense of being continuous. And just as discussed at the top, the patches neededn't be solid, we can for instance substitute sphere 0 of the shell child back to the tree child and sphere 1 of the tree child back to the shell child:

This produces a lot of variety, with three sets being blended (pale grey sphereical, grey craters and brown hills) and the two child sets overlapping. 

Are there ways to substitute neighbouring sets that aren't so restrictive? Or is there a way to ensure sphere order independence? It would be good to find out.