Fractions that recognise themselves through digit-splits and operations
Recreational Mathematics Pattern Discovery · v4.0
A selfie fraction N/D rewrites itself by splitting digits of N and D and applying an operation to each part, yielding the same reduced value. Numerator ops (2-part): A+B · A×B · A^B
Numerator ops (3-part): A+B+C · A×B×C · A×(B+C) · (A+B)×C · A×B+C · A+B×C · A^B+C · A+B^C · A^B×C · A×B^C Denominator ops: A+B · A+B+C · Numerator min can be set to 1; since splitting requires at least two digits, actual results naturally begin at N≥10.
Examples: 18/1782 = (1^8)/(17+82) = 1/99 · 289/561 = 2×(8+9)/(5+61) = 17/33 · 990/1155 = (9+9+0)/(1+15+5) = 6/7
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Insertion families start from a base selfie fraction and extend it by inserting a repeated block at a fixed position inside the denominator, producing a chain where every member is also a selfie fraction. 2-part denom:18/1782 → 18/17982 → 18/179982 → … (left part fixed, right part fixed) 3-part middle:130/1365 → 130/14365 → 130/144365 → … (left & right parts fixed, middle grows)
Obvious restarts, base fractions of the form a/(10a), and neutral numerator products such as 1×A are automatically excluded. Equivalent pairs 1^1 = 1×1 and 1^0 = 1+0 are each counted only once.
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Enter any fraction N/D to discover every selfie representation — all valid digit-splits and operations that reduce to the same value.
Run any search in tabs ①, ② or ③ first, then return here to download results as a .txt file. Each line is formatted as: k N/D = (num_op)/(denom_op);
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Run a search in tabs ①, ② or ③, then download the cleaned results as a modern .xlsx workbook. Separate columns contain the numerator, denominator, numerator expression, denominator expression, and complete pattern. Blank rows separate pattern families.
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A selfie fraction N/D can be rewritten as f(digits of N)/g(digits of D) giving the same reduced value.
Named by analogy: the same subject, captured from a different angle.