cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A349009 Decimal expansion of the area of the convex hull around the R5 dragon fractal.

Original entry on oeis.org

9, 7, 6, 1, 6, 4, 0, 0, 2, 9, 1, 2, 7, 0, 3, 5, 1, 3, 4, 0, 6, 4, 0, 7, 1, 5, 8, 0, 8, 4, 2, 1, 1, 1, 2, 9, 7, 2, 6, 3, 1, 2, 1, 9, 9, 3, 1, 7, 3, 2, 6, 9, 0, 5, 2, 4, 3, 4, 9, 4, 8, 8, 0, 3, 0, 0, 8, 2, 8, 7, 3, 8, 6, 7, 9, 6, 5, 1, 1, 6, 0, 1, 1, 0, 7, 5, 0, 4, 2, 4, 7, 8, 8, 5, 1, 6, 1, 5, 8, 6, 3, 8, 6, 6, 9
Offset: 0

Views

Author

Kevin Ryde, Nov 06 2021

Keywords

Comments

The fractal is taken scaled to unit length from curve start to end.
In the sum formula below, all HAtermf(j) > 0 and a simple upper bound is Sum_{j>=k} HAtermf(j) < 1/sqrt(5)^k.

Examples

			0.97616400291270351340640715808421112...

Links

Crossrefs

Cf. A349008 (finite areas), A349010 (fractal perimeter).

Programs

  • PARI
    \\ See links.

Formula

Equals 17/25 + Sum_{j>=1} HAtermf(j), where complex b=1+2*i and:
HAtermf(j) = (1/25)*(6*HAgrowf(1/b^j) + 2*HAgrowf((4+i)/b^j)),
HAgrowf(z) = MinReIm(ShearIm(RotQ(z))),
MinReIm(z) = min(abs(Re z), abs(Im z)),
ShearIm(z) = z + i*Im(z),
RotQ(z) = z if sign(Re z) = sign(Im z), or RotQ(z) = z*i otherwise.
Equals lim_{n->oo} A349008(n)/5^n.

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

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Nov 10 2021

Keywords

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

Crossrefs

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

Programs

  • PARI
    See Links section.

Formula

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

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

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, -1, -1, -2, -2, -1, -1, -2, -2, -1, -1, 0, 0, -1, -1, 0, 0, -1, -1, -2, -2, -3, -3, -2, -2, -3, -3
Offset: 0

Views

Author

Rémy Sigrist, Nov 10 2021

Keywords

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(1) = 0,
     a(2) = a(3) = a(14) = a(15) = a(18) = a(19) = 1.

Links

Crossrefs

Cf. A006496, A349008, A349009, A349010, A349195.

Programs

  • PARI
    See Links section.

Formula

a(5^k) = A006496(k) for any k >= 0.
Showing 1-3 of 3 results.

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