Symmetry is not simple. Before beginning your study, you must choose between reflection symmetry, rotational symmetry, translational, rotoreflection, or helical symmetries, point reflection and other involutive isometries. After which you may study nonisometric, scale symmetry and fractals. At which point my eyes are spinning and definitely not symmetrical.
Random lines and shapes have no place in symmetry. Symmetry is not self-similar like fractals but a near mirror reflection. It is correspondence in size, shape, and relative position of parts on opposite sides of a dividing line. The bell grading curve is an example. Symmetry is a desirable quality in tree pruning, butterflies, slinky toys, drilling augers and kaleidoscopes.
If you look in your bathroom mirror and draw a line down the middle of the reflection of your face, you will witness lack of symmetry however slight. Eyebrows situate at slightly different positions above eyes that fit into sockets at slightly different angles. While your nose is singular as is your nasal base and your nostrils are two, plastic surgeons can point out multiple opportunities for symmetry or lack thereof. As you transition from age six to sixty you will witness further erosion of your facial symmetry, and further evidence that we naturally lack perfection. As if we needed any proof.
All of which I found intriguing but unnecessary to appreciate the symmetry used in kaleidoscopes. A kaleidoscope utilizes reflection symmetry which is a point of intersection of two or more lines. This symmetry does not change or rotate. It is typically made of three rectangular lengthwise mirrors set at a 45-degree angle in a tube. The tube is then filled with bits of colored glass that tumble and display a symmetrical pattern as the tube is rotated.
Our fascination with a kaleidoscope begins with the material composition of the tube and bits of color tumbling inside. You can spend a few dollars or hundreds of dollars depending whether the tube is cardboard, wood or brass. The tube shape may vary in length and circumference thus also affecting the pattern and price. Perfectly intriguing.
If you would like to hang a kaleidoscope image on the wall, check out Dawn La Grave’s website www.lagravedesigns.com for a unique, artistic mathematical equation.