k-th Fibonacci's Signature

on 26 Oct 2021

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.');