In the 60s we didn't need no blinkin computer
Indeed. Ed Lorenz was able in 1963 to visualize the attractor behind deterministic nonperiodic flow with only rudimentary manual graph plotting done on basis of numeric printouts. And Mandelbrot wrote his pioneering papers on fractals (such as 'How long is the coast of Britain') in the middle Sixties, and although he was at IBM's Thomas J. Watson, the computing resources were those available at that time.
It's later than you think, the joint Russian-American space mission has already begun.