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 shapes and forms inherent to the spiral? The patterns you find are fundamental, archetypal and elegant.
Teachers, Introduce the concept of patterns and provide your students an interactive way to develop geometric sense, analyze and create patterns, and make connections between art and mathematics.
Artists, Use this pattern generator to produce naturalistic forms and shapes inherent to the helix.
How does it work?
This tool is based on phyllotaxis spirals and loosely on 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 = cos(a) + sin(a)
y = sin(a) + cos(a)
a is the angle at which a point is placed in relation to the previous point.
Do the patterns repeat? To answer this question, ask yourself if two snowflakes are ever alike. Can you find a pattern that has never been seen by human eyes?
It works best with an updated browser configured for HTML5.
- Steps - This takes you on a progression. Start and Stop affects this. Having the checkbox checked slows down the animation considerably.
- Radius - Sets the offset of the helix.
- Theta - This changes how the helix 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 equation to a semi-90 degrees
- 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 evenly. So, if you only have two colors, colors shift in an every-other pattern. If you have three colors, colors are distributed in a tri-sequence. This totally changes how the pattern looks, because the colors interfere in two or three steps. Also, if you turn one or two colors to white, neat overlapping 'white-space' designs occur.
Here are a few places to start. Enter these parameters, then adjust the Radius, Size, Alpha and Theta.
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.
View generator as standalone.