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Description
The Rainbow Dots (except Red) have entered the Lorenz attractor but not (yet) visited both lobes to form the famous "butterfly." Has Red Dot gone on strike? Is it injured? What's going on?! Actually, Red Dot starts at x=y=z=0 and the equations of the Lorenz system are such that, starting there means staying there. This behaviour is called a "fixed point," - a remarkably apposite name. The entire line x=y=0, z=any real number, behaves strangely, in fact. For any value of z, with z not equal to zero, and x=y=0, the motion will be directly towards x=y=z=0 but it slows down as it approaches and in fact will never actually arrive in any finite time interval. Meanwhile, starting arbitrarily close to x=y=z=0 but with x or y not actually zero, it's off to the Lorenz attractor you go, as the rest of the Rainbow Dots demonstrate.

Description
The Rainbow Dots (except Red) have entered the Lorenz attractor but not (yet) visited both lobes to form the famous "butterfly." Has Red Dot gone on strike? Is it injured? What's going on?! Actually, Red Dot starts at x=y=z=0 and the equations of the Lorenz system are such that, starting there means staying there. This behaviour is called a "fixed point," - a remarkably apposite name. The entire line x=y=0, z=any real number, behaves strangely, in fact. For any value of z, with z not equal to zero, and x=y=0, the motion will be directly towards x=y=z=0 but it slows down as it approaches and in fact will never actually arrive in any finite time interval. Meanwhile, starting arbitrarily close to x=y=z=0 but with x or y not actually zero, it's off to the Lorenz attractor you go, as the rest of the Rainbow Dots demonstrate.