WOLFRAM|DEMONSTRATIONS PROJECT

Minkowski's Question Mark Function

Minkowski's question mark function is a purely singular odd function of a real argument. If
[
a
0
;
a
1
,
a
2
,…]
is the simple continued fraction representation of the positive number
x
, then
?(x)
a
0
+2
n-1
Σ
n≥1
(-1)

a
1
+…+
a
n
2
. The value of the question mark function on the integers, rationals, or irrational quadratic numbers is rational. This Demonstration visualizes Minkowski's question mark function on the interval
(
x
0
,
x
0
+δ)
.