At first glance mathematics and art might appear very distant, perhaps even directly opposed to one another, but the fact is that they have quite a lot in common. How are they interlinked, and what do these links tell us?

The interest in prefabricated building modules is constantly growing due to the increasing possibilities of analysing extensive data sets in computers and the popularity of BIM technology. The ability to manage the position, size and properties of many different elements make it easy to create and evaluate complete modular models at the design stage. Benefits of prefabrication include, among the others, decreased cost, minimisation of environmental impact, and reduced labour on-site. However, making structures and buildings suitable for prefabrication puts additional responsibility on the designer, who needs to choose the modular system, partition the structure and prepare detailed schedules. The article refers to digital control over modular design in the context of the increasing complexity of structures. It focuses on methods and tools that either reduce the designer’s labour or provide him with information that can be used to optimise the structure in terms of efficiency or cost. The article organises the existing trends and presents three experiments on algorithmic control of modular structures to outline the differences in computational methods suitable for particular technologies: masonry, steel, glass and timber construction. The research illustrated in the article was undertaken in response to the need to develop construction technologies in line with the sustainable development trend.

Material of tesseraspids (Tesseraspidiformes) is reported from the uppermost Severnaya Zemlya Formation

(Lochkovian, Lower Devonian) of the Severnaya Zemlya archipelago, in the Russian Arctic, where it is associated

with other vertebrate remains, including corvaspids, acanthodians, and large but rare specimens of

osteostracans. The tesseraspid material is not abundant, and most often preserved as a “patchwork” of bony

platelets (tesserae), except for a few partly articulated specimens. We redescribe the holotype of Tesseraspis

mosaica Karatajūtė-Talimaa, 1983, whose head carapace is preserved as a flattened tube of adjacent tesserae.

This material is compared to the already published tesseraspid taxa, i.e., T. tessellata Wills, 1935, T. toombsi

Tarlo, 1964, T. mutabilis (Brotzen, 1934), T. oervigi Tarlo, 1964 emend. Dineley and Loeffler, 1976, T. denisoni

Tarlo, 1964, and T. talimaae Tarlo, 1965. All species are based upon rare and incomplete material, as no

head carapaces associated with trunk and tail are known, and so, the intraspecific variability is also unknown.

Distinction between “species” is based on the detail of the superficial sculpture of the tesserae of the head carapaces,

which is unsatisfactory. It is concluded that only four of the nominal species can be retained. A review

of all other known tessellated pteraspidomorphs indicates that our knowledge of tessellated heterostracans is

currently insufficient to support a meaningful classification.

The work reports on the development of random three-dimensional Laguerre-Voronoi computational models for open cell foams. The proposed method can accurately generate foam models having randomly distributed parameter values. A three-dimensional model of ceramic foams having pre-selected cell volumes distribution with stochastic coordinates and orientations was created in the software package ANSYSTM. Different groups of finite element models were then generated using the developed foam modeling procedure. The size sensitivity study shows that each of foam specimens at least contains 125 LV-cells. The developed foam models were used to simulate the macroscopic elastic properties of open cell foams under uni-axial and bi-axial loading and were compared with the existing open cell foam models in the literature. In the high porosity regime, it is found that the elastic properties predicted by random Laguerre-Voronoi foam models are almost the same as those predicted by the perfect Kelvin foam models. In the low porosity regime the results of the present work deviate significantly from those of other models in the literature. The results presented here are generally in better agreement with experimental data than other models. Thus, the Laguerre-Voronoi foam models generated in this work are quite close to real foam topology and yields more accurate results than other open cell foam models.