The Universe as a Tree
Posted: Sat May 19, 2018 10:49 am
Recent experiments have led me to search for a non-mathematical approach to creating an RS2 universe, as math works for very simple structures but rapidly becomes overwhelming when even minor complexity is introduced. This led back to a study of how computers model an artificial reality. There are a number of approaches, but one, in particular, matches RS concepts closely: the octree (octal tree) structure.
Octrees (or any n-dimensional tree structure) have many of the same properties as the RS: they are discrete (units of "voxels", volumetric pixels), has a minimum quantity of "1," possess a concept of "void" where nothing can exist (unit speed), are based on displacement and decomposition (reverse of "compounding") structure. Anything can be represented, emptiness, solid or fields, as the contents of a "voxel" can contain any properties. It can model 1D, 2D, 3D, 4D... any number of dimensions, using the same algorithms (dimensionally invariant), so it is of "general applicability." Issues like the "n-body" problem do not exist, because you are getting results from a geometric solution--not a mathematical one. This concept shows a lot of promise for RS/RS2-based models, much better than anything else I've tried over the last 25 years.
I have attached Donald Meagher's 1981 paper on octree encoding, as it is one of the best at describing the model.
It is also curious that many philosophies and spirituality refer to the Universe as a great tree, such as the Norse Yggdrasil. Perhaps, in their own way, they were right!
Octrees (or any n-dimensional tree structure) have many of the same properties as the RS: they are discrete (units of "voxels", volumetric pixels), has a minimum quantity of "1," possess a concept of "void" where nothing can exist (unit speed), are based on displacement and decomposition (reverse of "compounding") structure. Anything can be represented, emptiness, solid or fields, as the contents of a "voxel" can contain any properties. It can model 1D, 2D, 3D, 4D... any number of dimensions, using the same algorithms (dimensionally invariant), so it is of "general applicability." Issues like the "n-body" problem do not exist, because you are getting results from a geometric solution--not a mathematical one. This concept shows a lot of promise for RS/RS2-based models, much better than anything else I've tried over the last 25 years.
I have attached Donald Meagher's 1981 paper on octree encoding, as it is one of the best at describing the model.
It is also curious that many philosophies and spirituality refer to the Universe as a great tree, such as the Norse Yggdrasil. Perhaps, in their own way, they were right!