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k-th Fibonacci's Signature
on 26 Oct 2021
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k=4; % Order of the k-th generalized Fibonacci numbers
P=roots([1 str2num(repmat('-1 ',1,k))]); % Roots of the k-th golden numbers
[a,b]=ndgrid(-1:0.002:2*k,-0.01:0.002:k);
D=0;
sinu=figure();
for i=1:k
D=D+((P(i)-1).*P(i).^(a+1i*b-1))./(2+(k+1).*(P(i)-2)); % k-th Binet formula
end
pcolor(b,a,abs(angle(D)));
colormap(hsv)
shading interp
hold on
E=D(:,1);
plot(real(E),k*imag(E)/(max(imag(E)))+k,'k.');