Fibonacci's Last i-Dream

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

c=0:0.002:2*k;

[a,b]=ndgrid(c,c);

D=0;

josue =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

plot(real(D(:,1)),k*imag(D(:,1))/(max(abs(imag(D(:,1)))))+k,'k.-');