3D and density plots of the digits in various bases

Over the digit-base plane

3D plot of the first 200 digits of in various bases .

Density plot of the digits of in various bases . The gray level of the squares is .

Density plot of the digits of in various noninteger bases . The gray level of the squares is .

Density plot of cumulative sums modulo 2 of the digits of in various noninteger bases .

Digit averages and cumulative sums

Density plot of the average values of the digits of for various bases .

Density plot of the iterated cumulative sums , of the digits of modulo for various bases .

3D plots of the iterated averages , , odd (and a similar definition for even) of the digits of for and for various bases . No values are displayed in the right front corner because the initial digit sequence starts at and so does not allow to form symmetric average. For increasing iteration number , the averages approach .

Fourier series

Exponential Fourier series , over the ,‐plane. Here the are the digits of for various bases .

Pascal triangle modular plots

Density plot of the digits of for various bases . The first digits are extracted and arranged in a triangle and colored according to their value and their value modulo 2 and 3.

Power series plots

The function where the digits are .

3D plots of the power series for various bases . Here, is the th digit of in base . The left graphic shows the real part and the coloring is according to the imaginary part. The right graphic shows a contour plot of the argument over the complex plane and the coloring is cyclic.

Density plots of coefficients of of the power series for various bases . Here, is the th digit of in base , . The left graphic shows the coefficients modulo 2 and the right graphic shows the coefficients modulo

Density plots of coefficients of of the power series for various bases . Here, is the th digit of in base , . The left graphic shows the logarithm of the coefficients and the right graphic shows the fractional parts of the coefficients.