Complex base systems

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Donald Knuth in 1955 proposed quater-imaginary base ^[1]. It is a non-standard positional numeral system which uses imaginary number 2i as base. There are more bases we can use: i − 1 ^[2] which is one of periodic cases ^[3] — the fractional part is iterated function system which covers periodically the whole plane.

The construction of complex numbers we can get using 6 youngest bits in i + 1 (left) or i − 1 (right) base system

[edit] References

1. ^ D. Knuth. The Art of Computer Programming. Volume 2, 3rd Edition. Addison-Wesley. pp. 205, "Positional Number Systems"
2. ^ T. Jamil, The complex binary number system, IEEE Potentials, Volume 20, Issue 5, Dec 2001/Jan 2002 Page(s):39 - 41
3. ^ http://arxiv.org/pdf/0712.1309

[edit] See also

• Dragon curve

[edit] External links

• "Number Systems Using a Complex Base" by Jarek Duda, The Wolfram Demonstrations Project
• "The Boundary of Periodic Iterated Function Systems" by Jarek Duda, The Wolfram Demonstrations Project
• "Number Systems in 3D" by Jarek Duda, The Wolfram Demonstrations Project

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