Talk:Complex-base system

Image compression
There is a discussion about the use of this idea in image compression. 

periodic?
I preserved the phrase "is one of periodic cases" – but what does it mean? —Tamfang (talk) 00:32, 5 December 2008 (UTC)


 * Seeing no clarification, I'll remove the phrase but keep the footnote. —Tamfang (talk) 04:45, 16 December 2009 (UTC)

improve translation

 * Listed below are those of the system (as a special case shown above systems) and shows code numbers 2, -2, -1.

Whatever language this came from, it's not clear in English. Can someone improve it? —Tamfang (talk) 17:38, 3 May 2011 (UTC)

/* Complex_base_systems */
General notation: Instead of:
 * $$<\rho=\pm i\sqrt{2},[0,1]>$$

I would like to propose the notation:
 * $$\bigg\langle \rho=\pm i\sqrt{2},\{0,1\} \bigg\rangle$$.

The $$ \{0, 1\} $$ because it is a set, so that one can say: set of digits $$ D:= \{0, 1\} $$ and $$\big\langle \rho=\pm i\sqrt{2}, D \big\rangle$$, and the $$\big\langle ... \big\rangle$$ because of optics.

Text below: Shouldn't one split up into and
 * $$<\rho=\sqrt{2}e^{\pm i \pi / 2},B_2> $$, example, $$<\rho=[-1\pm i],[0,1]>$$ (see also section "Base −1±i" below).
 * $$\bigg\langle \rho=\sqrt{2}e^{\pm i \pi / 2},B_2 \bigg\rangle $$, example, $$\big\langle \rho=(\pm i\sqrt{2}),\{0,1\} \big\rangle$$.
 * $$\bigg\langle \rho=\sqrt{2}e^{\pm 3i \pi / 4},B_2 \bigg\rangle $$, example, $$\big\langle \rho=(-1\pm i),\{0,1\} \big\rangle$$ (see also section "Base −1±i" below). -- Nomen4Omen (talk) 11:42, 2 August 2011 (UTC)

Added reference
The inline reference to Penney's paper was wrong - it linked to some other paper. Unfortunately the system for inline references on Wikipedia is complicated enough that I don't have time to figure out how it works! So I added the bibliographical information on Penney's paper to the 'References' section in a very crude way. I hope someone can fix things up. John Baez (talk) 16:07, 8 November 2012 (UTC)

mixed radix
I've experimented with mixing the radices -1+i and -1-i. If they alternate, the rounding domain is a parallelogram with vertices at 0, 1, i, -1+i (or the conjugates); other sequences give other pretty shapes. —Tamfang (talk) 03:46, 3 March 2019 (UTC)


 * You mean radices alternating between -1+i and -1-i ?
 * Isn't a0*(-1+i)+a1*(-1+i)*(-1-i) = a0*(-1+i)+a1*2 very close to $$\big \langle 2i,\{0,-1+i,2,1+i\}\big \rangle$$ ? Which looks almost like the Quater-imaginary base system $$\big \langle 2i,\{0,1,2,3\}\big \rangle$$ ? --Nomen4Omen (talk) 11:04, 3 March 2019 (UTC)

animation
There may be a place for this – with a better caption – but not filling the top of the page. —Tamfang (talk) 06:14, 4 May 2024 (UTC)

rounding

 * The rounding region of an integer – i.e., a set of complex (non-integer) numbers that share the integer part of their representation in this system – has in the complex plane a fractal shape: the twindragon.

I would call it the truncation region. Rounding, it seems to me, is an arithmetic operation independent of base. —Tamfang (talk) 18:38, 1 July 2024 (UTC)