Branching system strategies for Discrete Geometrical Elements – II

  • Defining research aim (architecture/urbanism rather than engineering)
  • Non-voxel and non-honeycomb space filling with platonic solids
  • Supermesh – mesh morphing
  • Variation analysis (porosity, entropy, count, loop formations, empirical analysis)
  • Growth with highly constraining volume
  • Growth along guide paths
  • Urban/architectural development trajectories (with highly stressed notion of further research into multiple element library implementation
  • Phase III – Multi-element library + urb/arch development trajectories

Architecture is a man-made field which relatively recently transitioned from “a craft” towards a symbiosis of art and science – precisely this fact differs it from other fields. The most evident difference is the way it grows – while natural sciences focus on answering questions of nature and build-off from gathered answers to raise more questions towards what seems to be an infinite truth, architecture focuses on itself, thus the only way it can grow is to evolve by re-building itself. And it evolves in iterations, which we call cultural periods. Ever since architecture became more than a craft, it started evolving at the same rate as did the arts, thus periods such as Gothic, Baroque, Classicism were shared between all art forms and architecture at the same time but there has been a shift in 20th century, when the growth rate of the field of architecture started increasing. This does not mean that architecture became a field of science thus disconnecting from arts, but rather it started acting as a bridge between different disciplines. This enabled architecture to become a system of its own with as many influences and focus points for further growth as there are other disciplines.
Any decision that an architect makes is geometrical, because architecture – in its core – is a craft. We elevate and enrich the decision making process by raising questions from other disciplines. If the room is too dark we puncture a wall, that’s a geometrical move by an architect, but the question as well as the answer “why should the room be bright?” stems from the field of psychology. Another example would be – opening the ground floor of the building for the community increases the square meter cost of the remaining floors. The architect only makes a geometrical move, but the roots of that move are in sociology and economy.
An architectural research bridges architecture with (or acts as a bridge between) other disciplines to establish a new plethora of questions (and hopefully answers) enabling itself to evolve (grow) further.


Triangular Prism



Growth variation: face[0] transform to face[5] (0 deg) and face [7] (0 deg)



Growth variation: face[0] transform to face[6] (0 deg) and face [7] (0 deg)



  • 0% – ~17.02%

Planar structure with increasing entropy

  • ~17.02 – ~57.28%

Sinusoidal structure reconfiguration with increasing entropy

  • ~57.28% – ~71.34%

Empirically experienced 3-dimentional Chaotic behavior

  • ~71.34% – ~77.60%

Equilibrium range with asymmetrical spiraling behavior

Empirical observations point to similarity with Lorenz attractor behavior at ρ = 28, σ = 10, and β = 8/3

  • ~77.60% – 100%

3-dimensional crystalline pattern with decreasing entropy

Growth variation: face[0] transform to face[6] (0 deg) and face [7] (+60 deg)



  • 0% – ~50.30%

3-dimensional structure with pseudo-crystalline pattern with increasing entropy

  • ~50.30% – 99.(9)%

Equilibrium range with asymmetrical branching behavior and increasing planarity

  • 100%

Equilibrium node. Planar structure forming loops (reconnecting to “mother” cell) every 4 generations.

Additional notes:

  • 0% – 100%

Saddle type structure with increasing curvature values as well as entropy.

A break-point in entropy values can be observed once the structure starts folding into itself, which is directly influenced by the size of the structure (amount of growth generations).

entropy spike graph


Variation analysis – Porosity

X axis – Morphing percentage (0 to 100%)

Y axis – Density percentage (calculations tied to unified bounding boxes of aggregated strucutres, exept for calculations withing an isosurface based volume)




fig.# – All gathered information overlayed. Noticeable steep drop in density when morphing away from voxelized cube structure (0-5%) as well as increase in density when morphing towards platonic solid geometry morphology (90-100%) 


fig.# – Cube (0%) to Triangular prism (100%) morphing. Least amount of density drop within 0-5% gap. Highest density reached when growing in isosurface – partialy because of difference in calculation methods, partially because of elements properties.


fig.# – Cube (0%) to Tetrahedron (100%) morphing.

fig.# – Cube (0%) to Octahedron (100%) morphing.

fig.# – Cube (0%) to Icosahedron (100%) morphing.

Walkback method

Guide-curve following method