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The Artima Icon
A Base 16 Numeral System
by Bill Venners

The Artima icon is a Java applet that slowly counts from 0 to 15 in a numeral system that I dreamed up when I was in high school. I had been studying hexadecimal numbers and one day invented an alternate way to express base 16 numbers graphically, a set of numerals I named "hexabill."

Given that it is a Java applet, the Artima icon does not show up on many pages at artima.com. One of the most important ways to make a website user friendly is to make its pages download quickly. For this reason, Java applets should appear on web pages only if the applets are absolutely necessary. The Artima Icon applet does not qualify as absolutely necessary.

Here's the full Artima Icon applet:

For some reason, your browser won't let you view this way cool Java applet. artima.com

The Hexabill Numeral System

In hexabill, each numeral contains a vertical and horizontal line (like a plus sign) at its center. These crossing lines form four quadrants that are each assigned a power of two, as in:

Hexabill Powers of Two

To form the hexabill numeral for any of the base 16 "digits," 0 through 15 (decimal) or 0 through F (hexadecimal), simply connect the ends of the crossed lines for the appropriate powers of two. For example, the number 10 (decimal) is composed of 21 + 23, so the hexabill numeral for 10 has connecting lines in the quadrants for 21 and 23:

Hexabill Numeral Example

The quadrants in which a line is drawn are called closed quadrants, because these quadrants in effect contain a closed triangle shape. Quadrants in which no line is drawn are called open quadrants. In the example above for decimal number 10, quadrants 0 and 2 are open, quadrants 1 and 3 are closed.

Here are all 16 hexabill numerals:

Hexabill Numerals

The Artima Icon

In the Artima icon, the hexabill numeral is expressed in a more colorful way than the basic system described above. Rather than using a simple line to close a quadrant as shown above, the closed quadrants of the Artima icon are painted a solid color. To make the numeral still more colorful, the Artima icon changes its paint color each time it wraps around from 15 back to zero.

The Hexabill Player Applet

The applet below, Hexabill Player, lets you play with the variety of hexabill numeral that is used by the Artima icon:

For some reason, your browser won't let you view this way cool Java applet.

Click the "++" button to increment the number by one and the "--" button to decrement it by one. To make the numeral count with no further coaxing on your part, press the "Run" button. To stop the automatic counting, press the "Stop" button. Happy clicking.


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