Topographical Tessellation - Nick

Any quadrilateral can be tessellated hexagonally 3 ways by rotating it 180 degrees and placing like edges adjacent to each other.

We are assuming that we'll be making just one mold for one porcelain tile. Thus, bending this example up at each of the ends of the long axis and aggregating it produces some interesting gaps. An orthagonal plan view, or an elevation viewed from straight-on would seem closed, but viewed obliquely or from the side, cracks of negative space begin to open up and widen as the view shifts toward the side of the aggregated tiles.

In this example, I am most interested in looking at parallel projections of those oblique views, and using them as the basis for new aggregations (see top diagram in image above).



I am focusing on uses the base geometry of a two-part hexagonal tessellation made of a component trapezoidal tile to create a unit capable of interlocking tesselation.



Going through a series of steps to improve the aggregated form, I settled on a scheme for the tile, bottom left. Importing a background jpg to modo, I created a mesh based on the geometry. One advantage of modo here is that the primary parameter of aggregation (angles within the trapezoid) could be (for future iterations) edited very quickly and easily.



The other primary interest I am investigating is the potential for our translucent landscapes to become three dimensional. Raising some polygons in modo allows space for lighting within the porcelain "bulbs", as well as having the potential to create another geometric field condition.

There are two ideas guiding my plans for development of this form: first, now that the basic idea is laid out, to focus more on the negative space that is being created; and second, to really focus on the idea of topography. Today we should be learning to create a custom tool paths. The plan is that in effect, the tool path for this tile will be topographical contours. The inspiration that I am working off now is mountain ridges; I imagine the three dimensional bumps and protrusions working more like ridges with a more coordinated orientation. Already, there are tighter and looser regions within the aggregation.