“Wer sich an die Analyse der spätgotischen Bauform machen will, stößt alsbald auf eine negative Eigenschaft: die Spätgotik hat kein System; offenbar auch will sie keines haben.” - Georg Dehio

In contrast to the High Gothic, the late Gothic appears to be chaotic and disordered. The focus of this research is not on the manifestation of the building forms, but on the underlying generative principles. The preliminary statement is that if something can be generated by algorithms, it has indisputable a system, even if it is not visible on the result. The algorithms were created using Grasshopper 3D.

Fractal nature: top view of the 3D model created from the 15th-century plans of the north tower of the Stephanskirche, Vienna
Fractal nature: top view of the 3D model created from the 15th-century plans of the north tower of the Stephanskirche, Vienna

Basic geometries: some of the results of experiments with a 3 × 3 and a 5 × 5 grid
Basic geometries: some of the results of experiments with a 3 × 3 and a 5 × 5 grid

Basic geometries: experiment with recursive squares
Basic geometries: experiment with recursive squares

Basic geometries: generated plinth-like geometry
Basic geometries: generated plinth-like geometry

Basic geometries: generated towerish geometry
Basic geometries: generated towerish geometry

Randomly generated towers: an extract from the algorithm displaying the random generators
Randomly generated towers: an extract from the algorithm displaying the random generators

Some structures generated randomly using the same algorithm
Some structures generated randomly using the same algorithm

Complexity as a factor of height: the first four stages of the ‘growth’ of the tower drawn together. The basic structure, the crocketed one, the one with gables, and finally the first recursive level with the base structures again: the pinnacles around the octagon
Complexity as a factor of height: the first four stages of the ‘growth’ of the tower drawn together. The basic structure, the crocketed one, the one with gables, and finally the first recursive level with the base structures again: the pinnacles around the octagon

The first four stages animated

The first four stages animated
The first four stages animated

Complexity as a factor of height: the recursive stages. On the most complex one three recursive levels are present
Complexity as a factor of height: the recursive stages. On the most complex one three recursive levels are present

Recursive stages animated

Recursive stages animated
Recursive stages animated

The increase of complexity can be observed better when the different stages are side by side scaled to the same size
The increase of complexity can be observed better when the different stages are side by side scaled to the same size

The 1st, 4th and 7th tower of the previous image scaled to the same size and 3D printed. The printing was concluded at the University of Debrecen, Department of Civil Engineering
The 1st, 4th and 7th tower of the previous image scaled to the same size and 3D printed

Unintentionally created ‘mutant’ structures
Unintentionally created ‘mutant’ structures