Title

Chromatic Lands II PHI Dynamic Symmetry Armature plus Golden Spiral

Size

8x13

Price

Fibonacci Spiral applied to this PHI proportioned painting with a Dynamic Symmetry Armature. We intended the focal area to be the eye of the spiral, with foliage along the spiral to lead the viewer’s eye to that point. The ‘S’ of the path should also lead the eye around the painting. We note again the 8 and 13 are part of the standard Fibonacci series, with the ratios tending toward phi = 0,618…(8/13 = 0.615…, 13/21 = 0.619…, etc.).

Title

Chromatic Lands IV - Two PHI Grids side by side

Size

8x10

Price

Painting changed sufficiently to discard this armature. A slight modification of the DS grid, showing how two vertical PHI grids almost fit inside a 5:4 Dynamic Symmetry grid. In fact, if the painting were 1x1.25 (5:4 aspect ratio) then since the golden rectangles are 1x0.618..., we find that the two vertical golden rectangles are 1x.618.. + 1x.618 ..= 1x1.236 (close to 1x1.25)!!

Title

Land Abstraction I Dynamic Symmetry Armature Plus Golden Spiral

Size

8x13

Price

Near Golden Rectangle with the Fibonacci Spiral superimposed on the Dynamic Symmetry Armature. Note how the intersection of the main diagonal with its reciprocal coincides with the polar point of the spiral.

Title

Luminous Lands I Dynamic Symmetry Armature plus Golden Spiral

Size

12x19

Price

Dynamic Symmetry Armature plus Fibonacci Spiral with eye at the upper right. Another “PHI” painting, this time with two obvious focal points at the intersections of the main diagonals with their reciprocals. The diagonals seem to parallel the main path leading back to the mountains and the light curve crossing it up to the right cliff focal point. We see the repeated motif of the shadows and light forms paralleling the diagonal from the lower left up to the right. The eternal question to ask though: is the viewer’s eye drawn around the painting. Another question to ask is: is there a resting point? To me, the sky is a good restful area to pause for a few moments.

Title

Luminous Lands V Dynamic Symmetry plus Rabatment

Size

8x13 Aspect Ratio 2:1

Price

Dynamic Symmetry armature with Rabatment (dotted) squares. Painted "en plein air" before we began using the Dynamic Symmetry armature.

Back

Title

Luminous Lands VI Northern Lights PHI Dynamic Symmetry Armature plus Golden Spiral

Size

15x24

Price

The whirling squares are constructed within rectangles as they rotate around a point which we sometimes call the eye of the spiral (in this case at the upper right), following a golden spiral. The 24:15 Aspect Ratio (1.6) is close enough to the PHI Golden Mean of 1.618... A panel similar in size would be a 13x21 (two Fibonacci numbers) with a closer aspect ratio of 1.615... . The intent at the time of the painting was to place the focal point near the eye of the whirling square or golden spiral. Golden Rectangle with the Fibonacci Spiral superimposed on the Dynamic Symmetry Armature. Note how the intersection of the main diagonal with its reciprocal coincides with the polar point of the spiral.

Title

Luminous Lands VI Northern Lights - PHI Whirling Squares

Size

15x24

Price

The whirling squares are constructed within squares as they rotate around a polar point (in this case at the upper right), following a golden spiral.

Title

Turbulent Lands I Dynamic Symmetry Armature plus Golden Spiral

Size

10x16

Price

Note the approximate golden proportion of 16:10 (versus 16.18.. to 10). Circumstances prevented me from painting this in the field, but I spent much time thinking about the proportion and the subject based on photographs I took of the cliffs going up to Los Alamos. You can read a detailed account of the development of this painting on my blog at: Turbulent Lands: Design and Process.

Title

Turbulent Lands I - PHI - Dynamic Symmetry Armature

Size

10x16

Price

Title

Turbulent Lands II Dynamic Symmetry Armature plus Golden Spiral

Size

15x25

Price

We had 15x25 inch panels and felt that they were close enough in proportion to a golden mean (1.66.. rather than 1.618…) that we could attempt to make a larger version of Turbulent Lands I in the studio months later. After drawing the grid on the panel we continued by following the diagonals and horizontal and vertical lines with paint as much as possible. New techniques were used that merit a post on the blog. Look for one. Tools used were squeegees and other straight edge tools, trying to let the magic of the colors blend in in a fractal way. This technique might be called ‘fractured’. The Land Abstract Paintings in the booklet illustrate this technique also.

Title

Turbulent Lands II - PHI - Dynamic Symmetry Armature

Size

15x25

Price

Dynamic Symmetry Armature with added rebatement (dotted) lines.

Title

Turbulent Lands IV PHI Dynamic Symmetry Armature plus Golden Spiral

Size

10x16

Price

Painted ‘en plein air’ in Borrego Springs. I remember being very conscious of trying to place the focal point at the dominant shadow on the mountain on the upper right and using a spiral to lead the eye to that point (missed by a little). This was about the time that I first began consciously to paint a near-PHI proportioned panel.

Title

Turbulent Lands IV Whirling Squares

Size

10x16

Price

Golden rectangle. Whirling Squares with focal point in the upper right, near the intersection of the Baroque Diagonal and its reciprocal, the polar point of the Fibonacci Whirling Squares. Painted "en plein air" in Borrego Springs, Ca. At the time I was loosely identifying the polar point as the focal point so that the striking mountain shadow was seen as the focal area. We also used an implicit spiral to help identify landscape items that would help lead the eye around the canvas.

Title

Turbulent Lands V PHI

Size

15x24 Aspect Ratio near PHI

Price

We did not use the Dynamic Symmetry armature when designing this painting; however, the Golden Spiral was a significant part of the design, The curve of the spiral is not obvious here, but it begins at the upper left and spirals down to the bottom center and back up to the upper right. Then one can see the polar point of the spiral in the upper right. We would have preferred that it be a little lower. Next time we will use a panel with the spiral penciled in to be more precise.

Title

Turbulent Waters I - 4:3 Diagonals and Reciprocals

Size

12x16

Price

The dynamic symmetry theory suggests that the intersection of a main diagonal with its reciprocal (perpendicular line) is a good candidate for a focal point. In this case we are looking at two possibilities. Could this painting be improved if in fact the waterfall were closer to the upper right focal point 2? Would the composition be improved if the main diagonal (baroque from lower left to upper right). Let's see if we can break up the composition with horizontals and verticals and new diagonal line segments between intersection points that fits this particular composition.

Title

Turbulent Waters I - 4:3 Dynamic Symmetry Armature

Size

12x16

Price

Full dynamic symmetry armature with rebatement lines (dotted).

Title

Turbulent Waters I - 4:3 Dynamic Symmetry Armature with Markups

Size

12x16

Price

Added pink line segments to create a pattern. Is there one? Originally with this painting I began with a simple design, based on a fibonacci spiral. with the spiral ending in an focal point near the waterfall. I was curious to see if it follows a dynamic symmetry grid. In reality the line segments could be in the same direction as the diagonals of the DS. The grid's segments would be similar to the dynamic symmetry segments and so should be harmonious. Note of course that the armatures are getting more complex.

Title

Turbulent Waters II PHI Dynamic Symmetry plus Golden Spiral

Size

12x19

Price

The waterfall upper right focal point could be placed somewhat lower in the composition to lie at the intersection of the main diagonal with its reciprocal perpendicular line.

Title

Turbulent Waters IV Whirling Squares

Size

10x16

Price

PHI Rectangle. PHI Whirling Squares. Fibonacci Series. The water fall focal point is at the upper right intersection of the Baroque Diagonal and its reciprocal.

Title

Cloud Fractals Dynamic Symmetry plus Rabatment Armature

Size

12x16 Aspect Ratio 4:3

Price

4:3 Aspect Ratio Dynamic Symmetry plus Rebated Squares Armature. The upper right intersection of the Baroque Diagonal with its perpendicular reciprocal was chosen as the focal point. The contrast of the brightest light and the darkest cloud was emphasized at this point. Perhaps the foreground land could have been raised a little so that it aligned with a horizontal drawn through the lowest intersection of two of the reciprocals, We do note alignment of the different diagonals with the shape of the clouds. Historians have argued that with this kind of diagram with its may lines, it's natural that we will find this type of alignment. However, there were still many artists who enjoyed trying to use the geometry of the armature to guide them.

Back.