Caption for cover image
The cover depicts the striking fractal pattern formed by plotting the complex
zeros for all possible polynomials in powers of x with coefficients 1 and
1, up to degree 18. A wide variety of patterns and features become visible,
leading researchers to new mathematical solutions. See page XXX
for more details.

Figure 1a: Sensitivity of zeros for all polynomials with coefficients 1/1
up to degree 18 
Coloration is by sensitivity of the polynomials
to slight variation around the values of the zeros.
The color scale
represents a normalized sensitivity to the range of values; red is
insensitive to violet which is strongly sensitive. All zeros are pictured.

Figure 1b: Density of zeros for coefficients 1/1 
The zeros in figure 1a are colored by their local density. The range of color is
normalized to the range of densities; red is low density to yellow
which is high density.

Figure 1c: Sensitivity of zeros relative to coefficient a_{3} 
Figure 1a is reproduced, this time with sensitivity relative to the
x^{3} term. A subrange of the values is
highlighted, with the least sensitive zeros outside the range colored in white.

Figure 1d: Sensitivity of zeros relative to coefficient a_{9} 
Figure 1a is reproduced, this time with sensitivity relative to the
x^{9} term. Note that the banded features appearing across
the distribution of zeros are, to the best of knowledge, real and not
programmatic artifacts. However, their mathematical explanation
is not yet in hand.
