It's like exploring the microbiotic life of the Precambrian or flying among galaxies and nebula of space. Are you ready to take a virtual hike through the fundamental shapes and forms inherent to the spiral? The patterns you find are fundamental, archetypal and elegant.
The short film In the Design Jungle was accepted into Bridges 2017 interdisciplinary film festivan on art and mathematics.
How does it work?
This tool is based on one equation of the spiral. Many of the patterns display similarities with phyllotaxis spirals due to interference patterns as the spiral overlaps. Many of the spirals have structures that correlate with Fibonacci's sequence. As you walk through the three-dimensional sine wave (helix) you will notice that most permutations consist of 'white noise'. Every so often, a shape will appear within the dots pattern. This shape is a harmony of the sine-based 'spray' of interacting dots.
A good way to see how this pattern generator works is to set the Radius to 1 and Base to 1. Start increasing the size of the Base value and you'll notice the spiral begin to tighten its angle. Notice that after the Base is greater than about 200 patterns will begin appearing. Now increase the radius (the circle on which the spiral is placed. The patterns are simply a harmony of the visually interacting dots.
You can plot a simple version on a graph.
x= t*sin (t) - r*cos (t)
y= t*cos (t) + r*sin (t)
t is a set of variables, r is the radius of the initial spiral.
Do the patterns repeat? Are two snowflakes ever alike? Can you find a pattern that has never been seen by human eyes?
- Steps - This takes you on a progression. Start and stop affects this parameter.
- Radius - Sets the offset of the spiral.
- Theta - This changes how the spiral will twist within the Base.
- Base - This is the root of the equation. Steps and Theta rest on this value.
- Side View - This isn't a true side-view, but it shifts the spiral with a pseudo-3D effect.
- Dots - Dot value changes how many dots are generated for the interference pattern.
- Size - Dot size can fundamentally change how the dots interfere. Larger dots build interesting designs.
- Alpha - Having transparent dots can generate some really fascinating effects. For instance color mixing occurs for overlapping dots.
- Colors - Colors are spaced alternately around the spiral.
The development of this tool is a bit uncanny. As an oil painter, I was searching for a waveform to describe the highly abstract scene of the creation of the universe from Genesis 1:2. Sometimes I use software to generate nice forms, patterns and compositions. So when I came upon this elegant equation, I was truly amazed at the raw beauty that it produces. Not only is the equation very simple, it also creates patterns that are naturalistic in form.