The title just about sums it up how can I sub divide an equilateral triangle into many smaller equilateral triangles. I need all of the faces to be the same size and shape. Like a 2D pyramid made of many smaller 2D pyramids.
I could not yet figure out how to do it procedurally or in a non destructive manner. In the meantime you can easily do it by hand.
There is an addon shipped by default with Blender called Add Mesh: Extra Objects that can activated in the User Preferences dialog
Start by opening File > User Preferences > Addons then search for
Extra and activate the Add Mesh: Extra Objects addon.
Then in the 3D View press Shift+A > Add > Mesh > Math Function > Regular Solid.
By default it should already create a Tetrahedron, if not just pick it from the pulldown preset menu.
The just enter Edit Mode, select all faces, press W > Subdivide. Adjust Subdivision Number from the operator properties in the Toolshelf, or pressing F6