Geometrical DensityPerspective2020

More sophisticated shapes seem to conceal their rationale due to the multivariate sources and evolutionary tuning.
Buckminster Fuller understood that a strong and lightweight geodesic dome could be built with consistent elements. He provided a clear rationale and method to reach similar results. In contrast, parametric design tools have enabled the design of elaborate forms often independent of clear design pressures making their comparative evaluation difficult. Consequently, we are often the recipient of needlessly complex forms in architecture predominantly due to their visual appeal. Therefore we need a metric for complex forms.

If we evaluate a spectrum of designs we do not control between the atomic and planetary scales we can identify a geometrical pattern. Geometry undulates from spherical to highly differentiated and back to spherical following closely the inanimate-animate-inanimate categorization. For this spectrum to repeat a form at another scale, a pressure to derive the form must be very similar at both scales and this pressure must be a dominant force. Since electromagnetic forces and gravitational pull are both omnidirectional pressures, this spherical result at both ends of the spectrum is consistent with Fuller’s simple correlation between spheres and uniform strength.

Platonic solids similarly resolve very fundamental omnidirectional pressures evenly but contain a rationale for an exact number of faces. For instance, the electron valence shell of a Carbon atom contains four electrons and consequently their inherent magnetic repelling effect produces the tetrahedron. These simpler geometries are immune to evolution however, as we progress to the middle of the design spectrum, more sophisticated shapes seem to conceal their rationale due to the multivariate sources and evolutionary tuning. Nevertheless, a peak in differentiation can be seen in the middle with animate organisms that contain a number of systems (skeletal, nervous, integumentary...) linking together many scales (cell, tissue, organ, body). Therefore, while form may be weightless it can still correspond to an input density.

Architecture consequently operates at a lower differentiation than animate organisms and should similarly lack some differentiation relative to the peak as buildings will never respond to as many geometrical pressures. Due to the power of nascent parametric technology, we generate overly complex designs relative to the number of input pressures and this upper threshold should be monitored in a general sense. We also need to begin compiling a lengthy list of input forces that all buildings could potentially accommodate in order to comparatively evaluate a building’s geometrical density in detail without an evolutionary process in place. We can then share the absence or presence of a design consideration for each list element and more clearly interpret the value of complex designs.
Danielson Architecture Office

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