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GENESIS ONE.2 - User's Manual
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Design through mathematical functionIt'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 mathematics? 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.

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helix-roseHow does it work?

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 waves of dots.

A good way to see how this pattern generator works is to set the points to 1 and press play on the points. A spiral (helix) of dots is released one at a time. Notice that a pattern will begin appearing. This pattern is 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 a numeric progression (such as 1,2,3,4...)

Do the patterns repeat? To answer this question, ask yourself if two snowflakes are ever alike. I believe the answer is an astounding "no." Can you find a pattern that has never been seen by human eyes?

Although the classification of these shapes is somewhat arbitrary, since each form is related to the others in a great variety of ways, this family tree provides an adequate taxonomy to shapes and patterns available by using this tool.

System Requirements

The free Macromedia Flash Player version 6.0 or greater is required for the use of this tool.

Features

Scroll Bars

Begin by moving the increment scroll bar. This allows you to walk through small changes in the displayed pattern. Depending on how the base and interval are set, your 'walk' might be a stroll or a gallop. Press the division sign, to divide the number of steps by 100, up to three times. This new feature will allow you to slow down the movement through an animation.

Next try modifying the base. This scroll bar changes the fundamental pattern exhibited. In a sense, this scroll bar warps you to a different galaxy to explore.

The interval scroll bar is very similar to the base, but it seemingly makes smaller modifications to the exhibited pattern, like traveling within a galaxy.

For computers which have slow processors, you will need to set the points low, to 150 or less. The points scroll bar changes the number of points displayed on the screen. For machines with fast processors, you may enter a value in the points field and then hold down Enter. This can result in some very beautiful patterns.

The z-radius scroll bar spreads the circle of sine-waves outward so that the design expands. For best results, keep the z-radius open to about 90. The "z" part of the radius defines the z-axis aspect of this feature. When viewed from the side, a higher number will respond in a taller '3-D' form.

Lastly, the side view feature rearranges the pattern so a semi-3-D view is available. A few interesting patterns are viewable from a full 90-degrees, but this feature will simply help you understand how each shape is laid out along the z-axis. Viewing at 90 degrees can result in some beautiful design motifs.

Since I consider the development of this tool a discovery rather than a creation, it was difficult to determine how to name the modifiable variables within this tool. I hope these labels suffice.

Value Fields

You may enter values into the scroll bars' value fields. Remember to hold down Enter after entering a number into a field.

Play and Stop buttons

The play (red triangle) and stop (red square) buttons assist your travels. They are your 'cruise control' features. It is recommended that users with slower computers have patience with all of the buttons and features. When processing a dot pattern, there might be a delay when buttons are pressed. If you are having difficulties and the processing is too slow, hold down the Esc or Enter key to stop all play actions.

Presets

Up to 24 presets are available which store the location of your favorite patterns. Click a gray-colored preset to store a pattern. Yellow-colored presets have locations already associated with them. To clear a preset, double-click it. The green-colored preset is the currently-displayed preset.

On newer computers, presets are automatically saved to your machine as Flash cookies. If they are not being saved correctly, you will probably need to change Flash's Local Storage setting. Right-click in the window and then click the folder icon. Raise the Local Storage setting to at least 10%.

Color

Begin by clicking the color "on" button. The dot size will increase a bit and the background will become black. Scroll through the various scroll bars and seek a desired pattern. Color schemes can be shifted for the desired result through the use of the R (red), G (green) and B (blue) buttons. Each color can be advanced to 10 (~100%). After it reaches 10, it cycles back to -10 (~0%). Zero is defined as the normal color for the displayed image. The B/W button switches the background from black to white.

Recommendations

Start searching for a pattern with the points set low. Choose a base and an interval and press play on increments. When an interesting pattern emerges, stop the increments and raise the points value to expand the design. If desired, look at the pattern in color or obliquely using the side view scroll bar. If the Flash Player interrupts the processing, by stating that the Flash Player may cause your computer to become unresponsive, click "No" and Flash will continue to process a large image.

For fun, make a pattern come to life. Choose a base and an interval. Set the points and increments to zero. First press play on the increments, then press play on the points and see what happens.

Background

The creation 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. I never was able to paint that Genesis 1:2, but I did try Genesis 1:5.
 

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