eigenvalues-zero-one-matrices.sage

size = 4
valtab = []
for n in range(2^(size*size)):
    m = Matrix(QQ,size,size,[(n>>i)&1 for i in range(size*size)])
    for v in m.eigenvalues():
        valtab.append(v)
numtab = [N(v) for v in valtab]

numdict = {}
for v in numtab:
    if v in numdict:
        numdict[v] += 1
    else:
        numdict[v] = 1

maxcnt = max(numdict[k] for k in numdict)

pointlist = [point((real(v),imag(v)), color=Color(log(numdict[v])/log(maxcnt),0,1-log(numdict[v])/log(maxcnt)), size=sqrt(numdict[v])) for v in sorted(numdict.keys(), key=lambda k: -numdict[k])]

sum(pointlist).show(dpi=192, aspect_ratio=1)

roots-zero-one-polynomials.sage

size = 8
R = PolynomialRing(QQ,"x")
valtab = []
for n in range(2^(size)):
    p = R([(n>>i)&1 for i in range(size)]+[1])
    for (v,m) in p.change_ring(QQbar).roots():
        for j in range(m):
            valtab.append(v)
numtab = [N(v) for v in valtab]

numdict = {}
for v in numtab:
    if v in numdict:
        numdict[v] += 1
    else:
        numdict[v] = 1

maxcnt = max(numdict[k] for k in numdict)

pointlist = [point((real(v),imag(v)), color=Color(log(numdict[v])/log(maxcnt),0,1-log(numdict[v])/log(maxcnt)), size=numdict[v]) for v in sorted(numdict.keys(), key=lambda k: -numdict[k])]

sum(pointlist).show(dpi=192, aspect_ratio=1)