The 3D Illusion of 2D Regular Tessellations
Year: 2001 Authors: Imameddin Amiraslanov
Core claim
Regular tessellations can produce convincing depth and color illusions when viewed with two eyes, extending their aesthetic use in decorative design.
Topics
regular tessellations, 3D illusion, visual symmetry, color mixing
Domains
tessellations, symmetry, geometry, Op art, decorative patterns, architectural ornament, carpet design
Methods
binocular viewing, pattern repetition, color superposition, visual comparison
Media
geometric ornaments, color pictures, printed figures
Paper text
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BRIDGES Mathematical Connections in Art, Music, and Science
The 3D Illusion of 2D Regular Tessellations
Imameddin Amiraslanov Institute of Inorganic and Physical Chemistry Academy of Science, Husein Javid Avenu 31, Baku, Azerbaijan imam@gate.sinica.edu.tw
For the last several decades the Escher-like symmetry patterns have occupied wide area in the creative art. Strong geometrical basis, absence background, modality, regularity, using more and more new mathematical ideas, etc., have opened new aesthetic and applied avenues for this style.
I would like to emphasize one more peculiarity them, namely the 3D illusions of 2D regular tessellations. This illusion is based on viewing with two eyes. At focusing the eyes as shown in pic.1 we will see: a) normal;
a)
b)
In b) and c) the object seem to be further away. (Note that the filled circles represent the real object, that the while the hollow circles are the respective false images)
c)
d) and e) the images look closer.
d)
e)
For instance in pic.2a* we can easily prove that. Pic.2b and pic.2c show the method of making additional periods, where we can see analogical illusions simultaneously at several different planes from the looker. In the case of color pictures (pic.3**, as a result from the summation of existing colors we will observe new colors, which are absent in the original picture. May be this effect is one of the reasons of the high attractivity of medical architectural buildings, carpets, etc. decorated with geometrical ornaments.
Imameddin Amiraslanov
a)
b)
Pic.2
c)
Pic.3
- Pic.2 created by Imameddin Amiraslanov, Baku, Azerbaijan ** Pic.3 created by Jamal Jamalov, Baku, Azerbaijan