The Second Style also named the “Architectural Style”, can be recognized by the use of architectural elements painted in three dimensions. It was born from the First Style, improving it.

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The Context
The Second style or “illusionism” had decorated walls with architectural features and “trick of the eye” compositions. Many elements recall the First Style, but then this will change day after day and this style will develop its features. This technique is all about highlighting elements to give them a look at three-dimensional realities and this was a famous way of painting used in ancient Rome.

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It also features relative perspective, to give the idea of the “trompe l’oeil” in painting on the walls. The picture plane was pushed to the back on the wall by painted architectonic features such as Ionic columns or stage platforms. These wall paintings were used to widen the spaces in windowless Roman mansions.

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Images and landscapes began to be painted in the First style and then gained importance with illusionistic and architectonic motives. The decoration was used to create an important impression of depth. The landscape elements, in the end, covered the whole wall and so it looked like to the viewer as he or she was looking at a real scene. In the mature Second Style, the goal became to paint scenes of nature. Depth comes from the use of atmospheric perspective.
The Three Style Phases

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It is possible to distinguish several phases:
PHASE 1: The first phase of the Second Style was the introduction of depth as the main feature. It often included painted columns in front of an imitation marble wall or an illusionistic perspectival ceiling.
PHASE 2: In the second phase of the Second Style, painters started to experiment with more difficult ways of conceiving perspectives. The walls of the room went back into the painted space, creating the illusion of a room inside another.
PHASE 3: In this final Second Style phase, the whole wall was painted as illusionistic architecture with arches, vaults, and columns. This phase was also about the use of many exotic themes, like painted griffins, sphinxes, and fantastic creatures.

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This style opened up the wall by giving an illusion of windows and porticos which looked outward onto imaginary scenes painted with realistic shading and perspective, creating the illusion that one is looking through a window at the outside. Painted architecture in this style was heavy and substantial, with a multi-point perspective.
The Second Style Heritage
Examples of the Second Style are in the triclinium of the Villa Oplonti, in the Villa of the Mysteries, and frescoes from the Villa of Boscoreale, now hosted in the Metropolitan Museum in New York and the Archaeological Museum of Naples.

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Info sources: http://www.essential-humanities.net/western-art/painting/roman/