# Chris Bartlett

Professor of Art

Art Department, Towson University

Hunt Valley, Maryland, USA

Bartlett’s ‘chi’ ratio was discovered while analyzing the geometric composition of master paintings.

Chi is a unique ratio with similar generative properties as the golden ratio (phi) but its rectangle, instead of partitioning into a square and a phi rectangle, sub-divides into phi and chi rectangles. It has an aspect ratio of 1+√ (4phi+5)/(2phi) = 1: 1.355…

The compositional syntax of his paintings follows successive divisions into phi and chi rectangles and squares. The composition thus achieves coherence by creating a structure such that the elements of the painting are aligned within self-similar areas and consequently at repeating measures from each other, a unity through harmony of geometrically proportional areas.

Chi is a unique ratio with similar generative properties as the golden ratio (phi) but its rectangle, instead of partitioning into a square and a phi rectangle, sub-divides into phi and chi rectangles. It has an aspect ratio of 1+√ (4phi+5)/(2phi) = 1: 1.355…

The compositional syntax of his paintings follows successive divisions into phi and chi rectangles and squares. The composition thus achieves coherence by creating a structure such that the elements of the painting are aligned within self-similar areas and consequently at repeating measures from each other, a unity through harmony of geometrically proportional areas.

Chi Ratio: Greek Harbor 1

54 x 40 cm

Acrylic on canvas

2015

The painting begins with a chi ratio canvas.

The horizontal jetty splits the composition into a chi ratio rectangle at the top and a remaining phi ratio rectangle at the bottom. (This dissection can be obtained simply with a diagonal and one perpendicular to it from the opposite vertex). The division of the phi rectangle into its square and phi rectangle gives the vertical partition that governs the placement of the outboard and the man. The rebatment (folding the short side over the long to produce an interior square) composes the rails of the lower boats at the edges, and in turn below creates another square and phi rectangle at the base of the composition.

The horizontal jetty splits the composition into a chi ratio rectangle at the top and a remaining phi ratio rectangle at the bottom. (This dissection can be obtained simply with a diagonal and one perpendicular to it from the opposite vertex). The division of the phi rectangle into its square and phi rectangle gives the vertical partition that governs the placement of the outboard and the man. The rebatment (folding the short side over the long to produce an interior square) composes the rails of the lower boats at the edges, and in turn below creates another square and phi rectangle at the base of the composition.

Chi Ratio: Greek Harbor 2

54 x 40 cm

Acrylic on canvas

2015

The painting begins with a chi ratio canvas.

This horizontal harbor wall reverses the composition splitting into a chi rectangle at the bottom and the remaining phi rectangle at the top. The diagonal of the phi rectangle suggests the slope of mountain and roof. The phi rectangle is further sub-divided into its square on the left and phi on the right. That phi rectangle is again partitioned into its golden rectangle and a square. Its extrapolated diagonal creates the position of the vertical harbor wall at the left edge of a double square. The red buoy indicates the vertical division of the chi and phi rectangles of the lower chi rectangle.

This horizontal harbor wall reverses the composition splitting into a chi rectangle at the bottom and the remaining phi rectangle at the top. The diagonal of the phi rectangle suggests the slope of mountain and roof. The phi rectangle is further sub-divided into its square on the left and phi on the right. That phi rectangle is again partitioned into its golden rectangle and a square. Its extrapolated diagonal creates the position of the vertical harbor wall at the left edge of a double square. The red buoy indicates the vertical division of the chi and phi rectangles of the lower chi rectangle.