A349195 a(n) is the X-coordinate of the n-th point of the R5 dragon curve; A349196 gives Y-coordinates.

0, 1, 1, 0, 0, 1, 1, 0, 0, -1, -1, -2, -2, -1, -1, -2, -2, -3, -3, -4, -4, -3, -3, -4, -4, -3, -3, -4, -4, -5, -5, -6, -6, -5, -5, -6, -6, -5, -5, -4, -4, -5, -5, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -7, -7, -8, -8, -7, -7, -6, -6, -5, -5, -6, -6, -5, -5

Offset: 0

Author

Rémy Sigrist, Nov 10 2021

Keywords

• sign

Comments

The R5 dragon curve can be represented using an L-system.

Examples

			The R5 dragon curve starts as follows:
         +-----+
       24|   25
         |
         |
         +-----+     +-----+     +-----+
       23    22|   11|   10|    7|    6|
               |     |     |     |     |
             21|   12|    9|    8|     |
         +-----+-----+-----+-----+-----+
       20|   17|   16|   13|    4|    5
         |     |     |     |     |
         |     |     |     |     |
         +-----+     +-----+     +-----+
       19    18    15    14     3     2|
                                       |
                                       |
                                 +-----+
                                0     1
- so a(0) = a(3) = a(4) = a(7) = a(8) = 0,
     a(1) = a(2) = a(5) = a(6) = 1,
     a(9) = a(10) = a(13) = a(14) = -1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..3125
• Joerg Arndt, Matters Computational (The Fxtbook), section 1.31.5 Dragon curves based on radix-R counting.
• Kevin Ryde, Iterations of the R5 Dragon Curve, see index "point".
• Rémy Sigrist, Colored representation of the first 1 + 5^9 points of the R5 dragon curve (where the hue is function of the number of steps from the origin)
• Rémy Sigrist, PARI program for A349195
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A006495, A349008, A349009, A349010, A349196.

Programs

PARI

See Links section.

Formula

a(5^k) = A006495(k) for any k >= 0.