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

0,12

Comments

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

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

Formula

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A332380 A014678 A332381 * A164516 A351706 A016533

Adjacent sequences: A349192 A349193 A349194 * A349196 A349197 A349198

Keyword

sign

Author

Rémy Sigrist, Nov 10 2021

Status

approved