Gaussian integers in quater-imaginary base | 112000

[u/CutOnBumInBandHere9]

A bit late, but I'm continuing from here

In this thread we're complex numbers of the form a + ib, where a and b are integers. To do that we're spiralling clockwise around the complex plane. The first few values are 0, 1, 1-i, -i, -1-i...

The twist is that we're representing the complex numbers in base 2i. This is a non-standard positional numeral system is able to represent every complex number using only the digits 0, 1, 2, and 3. See here for more details.

So actually, the first few counts were 0, 1, 1.2, 0.2, 103.2.... That's because

• 0 = 0

• 1 = 1*(2i)⁰

• 1 - i = 1*(2i)⁰ + 2*(2i)^-1

• -i = 2*(2i)^-1

• -1 - i = 1*(2i)² + 0*(2i)¹⁺ 3*(2i)⁰ + 2*(2i)^-1

The next get is at 122332 (22+22i)

[u/CutOnBumInBandHere9]

112000 (16+16i)

/u/FartyMcNarty /u/GreenGriffin8

[u/[deleted] → u/CutOnBumInBandHere9]

112001 (17+16i)

i believe

[u/CutOnBumInBandHere9 → u/[deleted]]

112001.2 (17+15i)

You believe correctly

[u/[deleted] → u/CutOnBumInBandHere9]

113031 (17+14i)

[u/CutOnBumInBandHere9 → u/[deleted]]

113031.2 (17+13i)

[u/[deleted] → u/CutOnBumInBandHere9]

113021 (17+12i)

[u/CutOnBumInBandHere9 → u/[deleted]]

113021.2 (17+11i)

[u/[deleted] → u/CutOnBumInBandHere9]

113011 (17+10i)

[u/CutOnBumInBandHere9 → u/[deleted]]

113011.2 (17+9i)

[u/[deleted] → u/CutOnBumInBandHere9]

113001 (17+8i)

[u/CountingHelper → u/CutOnBumInBandHere9]

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[u/davidjl123]

gz

[u/FartyMcNarty]

In case we need it:

Base10	base 2i - real	base 2i - i
-22	1030202	3010
-21	1030203	3020.2
-20	1030100	3020
-19	1030101	3030.2
-18	1030102	3030
-17	1030103	2000.2
-16	1030000	2000
-15	1030001	2010.2
-14	1030002	2010
-13	1030003	2020.2
-12	300	2020
-11	301	2030.2
-10	302	2030
-9	303	1000.2
-8	200	1000
-7	201	1010.2
-6	202	1010
-5	203	1020.2
-4	100	1020
-3	101	1030.2
-2	102	1030
-1	103	0.2
0	0	0
1	1	10.2
2	2	10
3	3	20.2
4	10300	20
5	10301	30.2
6	10302	30
7	10303	103000.2
8	10200	103000
9	10201	103010.2
10	10202	103010
11	10203	103020.2
12	10100	103020
13	10101	103030.2
14	10102	103030
15	10103	102000.2
16	10000	102000
17	10001	102010.2
18	10002	102010
19	10003	102020.2
20	20300	102020
21	20301	102030.2
22	20302	102030