Python, 83 bytes
from turtle import* a,b=[i:=0],[-1] while 1:a,b=b,b+a;lt(b[i]**i*90);fd(5);i+=1 -6 thanks to tsh
Draws it infinitely.
Very slow because it generates another term of the Fibonacci sequence at every iteration. This is much faster if you want to test it:
from turtle import* a,b=[i:=0],[90] while 1: if i>=len(b):a,b=b,b+a lt(b[i]*(-1)**i);fd(5);i+=1 You can also add a speed(0) at the beginning to make it draw faster.
