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WOLFRAM|DEMONSTRATIONS PROJECT

Real Digits Carpet

​
horizontal
number
π
ϕ
C
K
A
1
2
1
3
3
1
3
vertical
number
π
ϕ
C
K
A
1
2
1
3
3
1
3
operation
Times
Plus
Subtract
BitAnd
BitOr
BitXor
power
mod
log
quotient
color scheme
Rainbow
plot type
MatrixPlot
ArrayPlot
base
10
length
10
numerator p
1
denominator q
2
numerator m
1
denominator n
3
window
A matrix of values is formed by successively applying a binary operation to the first 1200 real digits of two numbers expressed in a chosen base. That is, the
th
(i,j)
entry of the matrix is obtained by combining the
th
i
digit of the horizontal number with the
th
j
digit of the vertical number using the chosen binary operation. The matrix is displayed using either of Mathematica's built-in functions ArrayPlot or MatrixPlot. The frame ticks on the matrix plot are indices to the digits being viewed. A 2D slider controller lets you look at a portion of the large matrix in a window with size set by the "length" slider. The first and second rational numbers
p/q
and
n/m
in the top two rows of buttons are each set by sliders. The next numbers in the top two rows of buttons are
n
raised to the power of
p/q
and
n/m
raised to the power of
p/q
. These numbers will be irrational for most values of
p
,
q
,
n
, and
m
. The display is such that the element with the smallest indices is in the bottom left-hand corner.
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