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## 2/10/17

### Space, Transformations & Recursion.

Introduction.

... had insights that this has uses in Mathematics as well as in Physics, probably more.

... i was exploring Linear Algebra, Geometry & other fields of Mathematics - i plan to study Mathematics at Warsaw University in future as well, i plan to learn Physics from books after that, and other Sciences (Electronics, Chemistry, Biology, Nanotechnology, Nanoelectromechanical Systems - NEMS) as well.

Stitie Space is a 3D objects matrix with convenience methods to animate & transform objects within.

Stitie Space can be Recursive, as objects within can be treated as machines that can run Space(s) within; that way Space can be more dense at certain point(s) or continuously - as much as available resources allow; This can include GRIDs, as machine with Stitie Space objects can be Distributed & Recursive so it scales well with hardware/software infrastructure investments.

Non-Cartesian Spaces & Transformations.

By Space i understand a mathematical construct spanned by a linearly independent, minimal vectors set (a basis for a 'vector space').

i think that Space with Cartesian coordinates has two perpendicular axes, with consistently same unit of distance between values on each axis. i think we can abstract from this however, and talk about 'n-dimensional Cartesian Spaces' with an amount of n perpendicular axes.

Non-Cartesian Spaces do not neccessarily have perpendicular axes, might have different number of axes that two, it is not neccessary to have distance between points on each axis the same - can be more dense or sparse around certain point(s). It is also possible for points in Non-Cartesian Space to be in Relation(s), for example:

R = { 1 < 2, 2 > 3, 3 < 4, 4 < 2, ... };

Since we are using computers with a finite memory amount, we use discrete numbers for points & values on axes.

We also should use unambiguous 'position values' for points, not only an 'order relation' specified for these, as well.

One of future features planned for Stitie Space is space transformation(s) & projection(s) on different Cartesian or Non-Cartesian Spaces; this is about transformation, not only visualization in different Space(s).

Distance measuring between points in this/these Space(s) can be defined many ways as well (for example by number of 'hops' in the object graph, or by actual distance between objects when projected on the 'n-dimensional Cartesian Space').

Handling Many Objects at the same Coordinates.

With Recursion of Stitie Space, this can be done easily - a machine with object at coordinates creates Space(s) within, then 'sets up' multiple objects there at proper Coordinates, then concurrently manages interactions both within a Space, between objects in different Spaces within, and between object(s) within with the objects in the 'outer' Space(s).

Therefore Space Transformations can occur from any Space to any other Space, even if this potentially can cause 'collisions' of having multiple objects at the same Coordinates in the 'Result Space'.

Use example.

We can model gravity field around a 'magnet', where increases in 'attraction force' are higher near the magnet, and lose it's magnitude away from the magnet.

We might want to model Space with more dense coordinates near the magnet(s), and more sparse outside - to save the resources.

We might want to use transformation(s) as 'magnet(s)' move(s), using MATEN or/and Prism - Stitie Space's functionalities for transforming Space, or using other available ways as well - implemented already or planned in future.

See also, if You wish or need, ... : Stitie Machine 1.1 'Sunsail', Stitie Machine 1.2 'Satellite', Stitie Machine 1.3 'November Rain', Agile Transformation of Information State.