Thue-Morse: Difference between revisions
→{{header|Excel}}: Added an Excel LAMBDA version.
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=={{header|Excel}}==
===LAMBDA===
Binding the name '''thueMorse''' to the following lambda expression in the Name Manager of the Excel WorkBook:
(See [https://www.microsoft.com/en-us/research/blog/lambda-the-ultimatae-excel-worksheet-function/ LAMBDA: The ultimate Excel worksheet function])
{{Works with|Office 365 betas 2021}}
<lang lisp>thueMorse
=LAMBDA(n,
APPLYN(n)(
LAMBDA(bits,
APPENDCOLS(bits)(
LAMBDA(x,
IF(0 < x, 0, 1)
)(bits)
)
)
)(0)
)</lang>
and also assuming the following generic bindings in the Name Manager for the WorkBook:
<lang lisp>APPENDCOLS
=LAMBDA(xs,
LAMBDA(ys,
LET(
nx, COLUMNS(xs),
colIndexes, SEQUENCE(1, nx + COLUMNS(ys)),
rowIndexes, SEQUENCE(MAX(ROWS(xs), ROWS(ys))),
IFERROR(
IF(nx < colIndexes,
INDEX(ys, rowIndexes, colIndexes - nx),
INDEX(xs, rowIndexes, colIndexes)
),
NA()
)
)
)
)
APPLYN
=LAMBDA(n,
LAMBDA(f,
LAMBDA(x,
IF(0 < n,
APPLYN(n - 1)(f)(
f(x)
),
x
)
)
)
)</lang>
{{Out}}
The formula in cell B2 below defines the array of 2^5 = 32 bits which populates the range '''B2:AG2'''
{| class="wikitable"
|-
|||style="text-align:right; font-family:serif; font-style:italic; font-size:120%;"|fx
! colspan="33" style="text-align:left; vertical-align: bottom; font-family:Arial, Helvetica, sans-serif !important;"|=thueMorse(A2)
|- style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff;"
|
| A
| B
| C
| D
| E
| F
| G
| H
| I
| J
| K
| L
| M
| N
| O
| P
| Q
| R
| S
| T
| U
| V
| W
| X
| Y
| Z
| AA
| AB
| AC
| AD
| AE
| AF
| AG
|-
| style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff" | 1
| style="font-weight:bold" | Iterations
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| style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff" | 2
| style="font-weight:bold" | 5
| style="text-align:center; background-color:#cbcefb" | 0
| style="text-align:center" | 1
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 1
| style="text-align:center" | 0
| style="text-align:center" | 0
| style="text-align:center" | 1
|}
=={{header|Factor}}==
| |||