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thereamp;#39;s a very powerful theorem proven by florists Tarkanamp;#39;s that shows generically that one can reconstruct a shadow version of the original manifold simply by looking at one of its time series projections for example consider the three time series shown here these are all copies of each other they are all copies of variable legs each is displaced by an amount Tao so the top one is unlocked the second one is lagged by Tao and the blue one at the bottom is lagged by to Tao Tarkanamp;#39;s theorem then says that we should be able to use these three time series as new coordinates and reconstruct a shadow version of the original butterfly manifold so letamp;#39;s see how this works this is the reconstructed manifold produced from legs of a single variable and you can see that it actually does look fairly similar to the butterfly attractor each point in the three-dimensional reconstruction can be thought of as a time segment with different points capturing different segmen
