I have used the first month of 2021 to understand and explore the concept of symmetry, producing an image a day. Included are definitions, examples and some brief descriptions of techniques I found useful.
 I hope you get some creative ideas from this work.



Bilateral symmetry on a horizontal axis (reflection)
Left to right illustrates asymmetrical balance


Multiple bilateral axes are shown, common in reflection photos.
The swan is off-center, using the rule of thirds, which creates motion.

 Artistic Licence
Artistic Symmetry was used to compare and contrast across the vertical axis.


Collage
A print and it's mirror were collaged. This created a Rorschach. What do you see? 
The frame was added in Photoshop, then tonal adjustments and two color grading versions were made in Adobe Camera Raw.

3 Ways to make a mirror image
Left: paste up and copy,  Center: sandwiched transparencies (ie multiply)
Right: Photoshop, mirrored and masked layers. (Displayed sideways)

Building a symmetrical composite in Photoshop 
Left: Original to be cropped,  Center: Mirrored image was made with a created action (cropped to fit). Right: image rotated and the action reapplied. 
The result is symmetrical on both the vertical and horizontal axes.
Note the importance of the negative space in composites.

Ps Daily Creative Challenge: Symmetry   5.7.2020
Paul Trani taught an excellent introduction to the Photoshop symmetry Tool, Smart Objects and other techniques. This was my inspiration for this Project. Assets from Adobe. (Worth a watch: unlinked, copy and paste url)
www.behance.net/live/videos/5217/Photoshop-Daily-Creative-Challenge-Symmetrical-Design


 The trees were copied Dual Axis, then the Photoshop Dual Axis Symmetry tool was used. (above)
 A Photoshop action was applied to each image. (above)
Reflection times 4.  A horizontal translation (tiling) of a 
Dual Axis Symmetry created two more vertical axes.



 At first look, Dual Axis and Radial Symmetries look similar, but there are significant differences. The left hand drawing shows the upper left quadrant original, center how it is copied dual axis and right as a radial rotation. (1) shows reflection or direction of rotation. The greatest differences are along the 2 axes. On the diagonals or medians (M), symmetrical shapes aligned with it (2) stay the same, but if moved they are rendered differently (3). The squiggly lines (4) are reflected both ways across each axis (center), but rotated in the radial example (Right). The first and third quadrants are identical in each example. I like to think of Dual Axis as flipping a copy across the next axis, and Radial as rotating, from center, a copy into the next section. Examples shown below.

          
            Dual Axis                                                                                             Radial

More Radial Symmetry
Left: Radial Symmetry Tool.  Center: Rotated photograph.  Right: Library/ 
Create from Image/ pattern, plus the Radial Symmetry Tool.


The Shape tool created the disk and star.
 I painted the center with the Radial Symmetry Tool.

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Left: 5 Axis Radial Mandala                                         Right: Traditional 4 Axis Mandala

All Ps Symmetry tools reflect across a line or axis. The Mandala tool copies that result and rotates it from the center, producing radial symmetry. An even number of axes also shows bilateral symmetry, any multiple of 4 produces Dual Axis Symmetry (above right). A similar algorithm is used by Ps Library/ + / patterns, allowing the sampled photo to be combined with brush work in a Mandala, or other symmetry tool layer. Set the Patterns to 0 or 45 degrees. In layers, alignment of the center points and the angle of the axes is critical.



HORIZONTAL TRANSLATION
 Time lapse of a Great Blue Heron in flight

PATTERNS
Patterns are an example of Translational Symmetry. All these patterns were sampled from a single photo using the Photoshop/ Library/ + / create from image/ pattern tool.

GLIDE REFLECTION
is a reflection over a line, then translation over the line in a single operation. (below)


Symmetry
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Symmetry

Symmetry, a tutorial defining different types of symmetry and using Photoshop to create examples, employing various techniques. Original Photos, Read More

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