REVIEW: THE AMAZING WORLD OF M C ESCHER
This article analyses the different visual themes explored by M. C. Escher in his artwork. Click on a section to jump forward.
- Regular Solids
- Impossible Shapes
- Further Information
Introduction: The Amazing World of M. C. Escher
A selection of 91 works of art, from 1919 to 1969, are hung in chronological order throughout three rooms. Central islands display Escher’s additional development work, notes and letters.
From 1919 to 1935 Escher focussed on mastering techniques. Using architectural landscape, portraiture and still life, he developed a wide range of print making skills – particularly in woodcut and lithography.
From 1935 to 1969 he used these techniques to explore different themes: tessellation, perspective, regular solids, reflection, impossible shapes and infinity.
The following review focusses on this latter period, demonstrating how Escher explored and developed these themes within his art.
A tessellation is defined as a shape that can be repeated without gaps or overlaps to cover a surface. Escher referred to this as ‘regular division of the plane’.
While some of Escher’s early work included symmetry and pattern, he didn’t create his first real tessellation until 1925, after visiting the Moorish palace, Alhambra, in Granada, Spain.
Escher copied the patterns of the Alhambra. He used them to define his own classification system and inspire new designs.
By understanding the rules behind tessellation he developed shapes into recognisable figures.
‘Metamorphosis I’ uses two tessellating shapes: a cube (whose outline is a regular hexagon) and ‘China Boy’. By manipulating the shape over progressive steps, Escher morphs one tessellation into the other. The cubes also blend into Atrani, an Italian town he had visited several times.
Escher combined tessellation with other themes he was interested in. ‘Reptiles’ features a dodecahedron – a regular solid not found to exist naturally.
The circling reptiles hint at Escher’s interest in infinity. The use of a mobius strip (a real shape with only one side) in ‘Horseman’, however, means that the pattern is actually infinite.
Tessellation gave Escher a set of parameters that he applied to create artwork. Combining this with other themes, such as infinity, furthered his investigations in geometry.
The use of architecture and vanishing points form the basis to Escher’s work in perspective.
In 1936, Escher visited La Mezquita, The Great Mosque of Cordoba, in Spain.
His sketch shows two clear corridors along the pillared archways. In reality, it is only possible to see one. This subtle manipulation of perspective is something Escher continued to develop.
‘Still Life and Street’ is a combination of two images. The ‘still life’ foreground and the ‘street’ background share the same vanishing points. With the grain of the table running into the diagonal texture of the street, the two images combine seamlessly to make one.
‘Relativity’, again, uses one set of vanishing points – but this time to combine three images.
The form resulting from the staircases, is a possible shape. What makes it impossible, is the simultaneous presence of three directions of gravity.
‘Print Gallery’ warps perspective by removing the parameters of fixed vanishing points altogether. Escher creates an image where the inside (on the left of the picture), becomes the outside (on the right).
Throughout his work on perspective, Escher manipulated fixed parameters such as vanishing points and gravity. Although the perspectives he created may seem unreal, they are representative of a world where his rules apply.
While tessellating polygons form naturally in crystalline structures, they can also be repeated to make surfaces of regular solids. Order such as this, was a source of great inspiration for Escher.
Escher experimented by combining these shapes to create new ones. The main shape in ‘Stars’ consists of three interlocking octahedrons (an eight sided shape made from triangular surfaces). Floating around it are several more shapes of various regular solid combinations.
‘Double Planetoid’ takes the concept one step further. Two tetrahedrons (a shape with four triangular faces) are combined to create two separate worlds: one of nature and one of civilisation.
In ‘Contrast’, Escher juxtaposes the order of regular solids with chaos.
Regular solids offered Escher a symbol of simplicity and order in his artwork.
Escher often used everyday objects and observations to inspire his work. His interest in how light reflected not only revealed the form of the subject matter itself, but also of the objects surrounding it.
‘Three Spheres II’ demonstrates that objects of identical form alter in appearance due to how light reflects from their differing surfaces. The central sphere reflects the entirety of it surrounds, whilst the one on the right reflects nothing.
In ‘Rippled Surface’ the water’s disturbed form is only apparent due to the reflection of the trees and moon. At the same time, the trees and moon are only visible due to the water’s reflection.
‘Three Worlds’, again, uses the reflected images of trees on water. Floating leaves, instead of ripples, define the water’s surface. A third ‘world’ is added beneath the surface of the water in the form a carp.
Escher’s work on reflection challenges our visual perception of objects due to the effects of light and surfaces.
A self-confessed non-mathematician, Escher did, however, borrow ideas from the world of mathematics to inspire his work.
Belvedere not only applies impossible mathematical shapes, but explains the principle behind them at the same time. The man at the bottom of the tower is holding the impossible shape from which the structure behind him is inspired. In front of him is a sketch which highlights how the impossible shape is conceived.
Pillars at the back of the structure, shift to the front – and vice versa. The result? Perfect, geometric madness. Inspired further by the publications of mathematicians L. S. and R. Penrose, Escher continued to bamboozle his audience. From a specific viewpoint, the ‘Penrose Steps’ creates an illusion of a continuous staircase. If the steps are viewed at a different angle, a gap at the back of the staircase is revealed.
Escher applied this principle to ‘Ascending and Descending’.
The ‘Penrose Triangle’ uses similar principles to those in Belvedere. Lines which should connect edges to the front of the shape, connect to the back – and vice versa.
Escher applied the ‘Penrose Triangle’ to ‘Waterfall’. It resulted in a perpetual flow of water which Escher explained would only need to be refilled due to the effects of evaporation.
Escher’s keen understanding of geometry allowed him to implement emerging ideas from the world of mathematics into his artwork.
Towards the end of Escher’s life, his focus was drawn, almost solely, to the ultimate parameter: infinity.
Inspiration was drawn from the mobius strip – a shape with one side and one edge. A train of marching ants follows the never-ending surface.
As with impossible shapes, Escher employed ideas from the world of mathematics. H. S. M. Coxeter’s hyperbolic geometry publication demonstrated infinity in a graphical sense. As the triangles reach the edge of the circle they become infinitely small.
This publication, along with Escher and Coxeter’s subsequent correspondence, assisted the creation of the ‘Circle limit’ series. But instead of triangles, Escher, of course, used his own tessellations.
‘Snakes’ was Escher’s final work. The interlinking circles decrease in size, both towards the centre and towards the outer edge. This creates two infinity limits.
Escher explored infinity by applying and manipulating mathematical principles.
Common factors that link Escher’s themes are rules and process. They combine to make order.
Rules gave Escher inspiration and drive. They can be used to clearly and precisely define the themes of his work: tessellation, perspective, regular solids, reflection, impossible shapes and infinity. Example: Correspondence with mathematician, H. S. M. Coxeter, to establish laws of hyperbolic geometry.
Escher followed the same working process for all of his themes: copying, applying and manipulating.
Copying: Escher acquired knowledge through copying. He not only made studies from objects and scenes from the world around him – but also from geometric patterns and mathematical concepts. Example: Copying the tessellating patterns from the Alhambra, Cordoba, Spain.
Applying: Escher applied his studies to his artwork. Example: Application of the mathematical concept of the Penrose Steps in ‘Ascending and Descending‘.
Manipulating: By altering and reapplying rules, Escher created representations of alternative realities. Example: He manipulated both perspective and geometry in ‘Print Gallery‘.
By combining rules and process Escher maintained order. Whether his work is perceived as real, imaginary, possible or impossible – the dominating force of order is ever present. Escher, himself, puts it best:
“The desire for simplicity and order helps us to endure and inspires us in the midst of chaos; chaos is the beginning, order is the conclusion.”
If you would like to buy Escher inspired artwork on canvas or in print, you can visit Tessellation Art.
For further information about the ‘The Amazing World of M. C. Escher’, you can visit the Dulwich Picture Gallery.
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All M.C. Escher works © 2015 The M.C. Escher Company – the Netherlands. All rights reserved. Used by permission. www.mcescher.com