The first of his great insights was the discovery that the extraordinarily complex almost pathological structures, which had been long ignored, exhibited certain universal characteristics requiring a new theory of dimension to treat them adequately which he had generalised from earlier work of Hausdorff and Besicovitch but the second great insight was that the fractal property so discovered, the general theory of which he had provided, was present almost universally in Nature.
Ang unang ng kanyang magandang pananaw ay ang pagkatuklas na ang extraordinarily kumplikadong halos pathological estraktura, na kung saan had been long pinansin, exhibited ilang pandaigdig na katangian na nangangailangan ng isang bagong teorya ng sukat sa paggamot sa mga ito adequately na niya generalised mas maaga mula sa trabaho ng Hausdorff at Besicovitch ngunit ang pangalawang magandang pananaw ay ang ari-arian fractal kaya natuklasan, ang pangkalahatang teorya ng na ibinigay niya, ay kasalukuyan halos lahat ng dako sa Nature.