Cantor set: Difference between revisions
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→{{header|Excel}}: Added a draft in terms of Excel LAMBDA expressions |
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Same result of Java |
Same result of Java |
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=={{header|Excel}}== |
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===LAMBDA=== |
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Binding names to the following lambda expressions in the Name Manager of the Excel WorkBook: |
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(See [https://www.microsoft.com/en-us/research/blog/lambda-the-ultimatae-excel-worksheet-function/ LAMBDA: The ultimate Excel worksheet function]) |
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{{Works with|Office 365 betas 2021}} |
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<lang lisp>CANTOR |
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=LAMBDA(n, |
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APPLYN(n)( |
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LAMBDA(grid, |
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APPENDROWS(grid)( |
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CANTOROW( |
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LASTROW(grid) |
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) |
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) |
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) |
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)({0,1}) |
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) |
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CANTOROW |
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=LAMBDA(xys, |
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LET( |
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nCols, COLUMNS(xys), |
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IF(2 > nCols, |
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xys, |
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IF(3 < nCols, |
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APPENDCOLS( |
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CANTORSLICES(TAKECOLS(2)(xys)) |
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)( |
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CANTOROW(DROPCOLS(2)(xys)) |
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), |
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CANTORSLICES(TAKECOLS(2)(xys)) |
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) |
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) |
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) |
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) |
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CANTORSLICES |
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=LAMBDA(ab, |
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LET( |
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a, INDEX(ab, 1), |
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b, INDEX(ab, 2), |
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third, (b - a) / 3, |
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CHOOSE({1,2,3,4}, a, a + third, b - third, b) |
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) |
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) |
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SHOWCANTOR |
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=LAMBDA(grid, |
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LET( |
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leaves, LASTROW(grid), |
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leafWidth, INDEX(leaves, 1, 2) - INDEX(leaves, 1, 1), |
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leafCount, 1 / leafWidth, |
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SHOWCANTROWS(leafCount)(grid) |
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) |
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) |
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SHOWCANTROWS |
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=LAMBDA(leafCount, |
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LAMBDA(grid, |
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LET( |
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xs, FILTERP( |
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LAMBDA(x, NOT(ISNA(x))) |
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)( |
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HEADCOL(grid) |
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), |
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runLengths, LAMBDA(x, |
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CEILING.MATH(leafCount * x))( |
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SUBTRACT(TAILROW(xs))(INITROW(xs) |
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) |
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), |
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iCols, SEQUENCE(1, COLUMNS(runLengths)), |
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CONCAT( |
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REPT( |
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IF(ISEVEN(iCols), " ", "█"), |
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runLengths |
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) |
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) & CHAR(10) & IF(1 < ROWS(grid), |
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SHOWCANTROWS(leafCount)( |
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TAILCOL(grid) |
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), |
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"" |
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) |
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) |
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) |
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)</lang> |
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and also assuming the following generic bindings in the Name Manager for the WorkBook: |
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<lang lisp>APPENDCOLS |
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=LAMBDA(xs, |
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LAMBDA(ys, |
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LET( |
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nx, COLUMNS(xs), |
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ny, COLUMNS(ys), |
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colIndexes, SEQUENCE(1, nx + ny), |
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rowIndexes, SEQUENCE(MAX(ROWS(xs), ROWS(ys))), |
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IFERROR( |
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IF(nx < colIndexes, |
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INDEX(ys, rowIndexes, colIndexes - nx), |
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INDEX(xs, rowIndexes, colIndexes) |
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), |
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NA() |
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) |
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) |
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) |
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) |
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APPENDROWS |
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=LAMBDA(xs, |
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LAMBDA(ys, |
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LET( |
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nx, ROWS(xs), |
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rowIndexes, SEQUENCE(nx + ROWS(ys)), |
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colIndexes, SEQUENCE( |
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1, |
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MAX(COLUMNS(xs), COLUMNS(ys)) |
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), |
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IFERROR( |
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IF(rowIndexes <= nx, |
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INDEX(xs, rowIndexes, colIndexes), |
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INDEX(ys, rowIndexes - nx, colIndexes) |
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), |
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NA() |
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) |
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) |
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) |
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) |
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APPLYN |
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=LAMBDA(n, |
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LAMBDA(f, |
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LAMBDA(x, |
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IF(0 < n, |
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APPLYN(n - 1)(f)( |
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f(x) |
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), |
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x |
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) |
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) |
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) |
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) |
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DROPCOLS |
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=LAMBDA(n, |
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LAMBDA(xs, |
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INDEX( |
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xs, |
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SEQUENCE(ROWS(xs), 1), |
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SEQUENCE(1, (COLUMNS(xs) - n), 1 + n, 1) |
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) |
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) |
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) |
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FILTERP |
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=LAMBDA(p, |
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LAMBDA(xs, |
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FILTER(xs, p(xs)) |
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) |
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) |
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HEADCOL |
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=LAMBDA(xs, |
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LET(REM, "The first item of each column in xs", |
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INDEX(xs, 1, SEQUENCE(1, COLUMNS(xs))) |
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) |
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) |
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INITROW |
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=LAMBDA(xs, |
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INDEX( |
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xs, |
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SEQUENCE( |
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1, |
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COLUMNS(xs) - 1, |
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1, 1 |
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) |
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) |
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) |
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LASTROW |
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=LAMBDA(xs, |
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INDEX( |
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xs, |
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ROWS(xs), |
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SEQUENCE(1, COLUMNS(xs), 1, 1) |
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) |
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) |
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SUBTRACT |
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=LAMBDA(a, |
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LAMBDA(b, a - b) |
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) |
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TAILCOL |
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=LAMBDA(cols, |
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LET(REM, "The tail of each column in the grid.", |
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INDEX( |
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cols, |
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SEQUENCE(ROWS(cols) - 1, 1, 2, 1), |
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SEQUENCE(1, COLUMNS(cols)) |
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) |
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) |
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) |
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TAILROW |
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=LAMBDA(xs, |
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LET(REM,"The tail of each row in the grid", |
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n, COLUMNS(xs) - 1, |
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IF(0 < n, |
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INDEX( |
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xs, |
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SEQUENCE(ROWS(xs), 1, 1, 1), |
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SEQUENCE(1, n, 2, 1) |
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), |
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NA() |
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) |
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) |
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) |
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TAKECOLS |
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=LAMBDA(n, |
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LAMBDA(xs, |
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INDEX( |
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xs, |
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SEQUENCE(ROWS(xs)), |
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SEQUENCE(1, n) |
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) |
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) |
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)</lang> |
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{{Out}} |
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As a string, with the format of the cell set to a mono-spaced font, and with Format > Cells > Alignment > Wrap text = True, to allow for the display of Excel's (platform - independent) CHAR(10) line breaks: |
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{| class="wikitable" |
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|- |
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|||style="text-align:right; font-family:serif; font-style:italic; font-size:120%;"|fx |
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! colspan="2" style="text-align:left; vertical-align: bottom; font-family:Arial, Helvetica, sans-serif !important;"|=SHOWCANTOR(CANTOR(3)) |
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|- style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff;" |
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| |
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| A |
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| B |
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|- style="text-align:right;" |
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| style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff" | 1 |
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| style="text-align:right; font-weight:bold" | |
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| style="text-align:left; font-weight:bold" | Cantor set level 3 |
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|- style="text-align:right;" |
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| style="text-align:center; font-family:Arial, Helvetica, sans-serif !important; background-color:#000000; color:#ffffff" | 2 |
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| style="text-align:right; font-weight:bold" | |
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| style="background-color:#cbcefb;" | <lang>███████████████████████████ |
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█████████ █████████ |
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███ ███ ███ ███ |
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█ █ █ █ █ █ █ █</lang> |
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|} |
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=={{header|Factor}}== |
=={{header|Factor}}== |
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