### Self-organization of vectors

Here is the interactive EightPoints machine, starting with 7 bivectors (Ex. No. 18). Depending on the chosen example the machine uses up to 22 bivectors, each with two points. The algorithm (watch p. 1) simulates a strong coupling of the bivector points, thus the "center of mass" and the "torque" remain constant. All 8 points are also weakly coupled by containing an electric charge (e.g. -3, +2 units). If Pull > 0, this influences the attractor figure, too. The law for charged particles is, that the force of the interaction between them is attractive if they have opposite signs and repulsive if like-signed.

The EightPoints Machine

Use the control panel below the drawing area to take influence on the image. In detail:

• Click the button New, if you only see a diffuse picture. This will determine new random values ​​for the points.
• If you recognize parts of an attractor, multiple use of the button Draw often results in a stabilization.
• If a stable attractor does not move after clicking, you can use Draw+ to intensify the image.
• Reset resets the values of the actual example.
• With the Scale value you can adjust the image size (1 = 100%, 0.5 = 50%, etc.).
• If you increase the parameter Pull, parts of the figure are moved (charge influence q0 - q7).
• Shift the image left/right and up/down by ±dx and ±dy pixels.
• Define the electric charges of the eight points.
• Change the Dimension (Dim) - the number of components of each point.
• With the Cmd input field there are even more influence options.

Pull ±dx ±dy

Scale Cmd

Graph

q0 q1 q2 q3 q4 q5 q6 q7 Charges Dim

Programmers may download the HTML page code, the commented javascript source code, and modify the values in the function "this.examples".

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© 2020 Ulrich Schwebinghaus