Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
“Figure 1: Left panel: Chaotic attractor of a driven anharmonic oscillator on the location-position plane of a stroboscopic map taken with the period of the driving. Right panel: Natural measure on the same chaotic attractor. Lighter colors indicate higher local values of the distribution. Both the attractor and the natural measure are fractal. (From T. Tel, M. Gruiz, Chaotic Dynamics, An Introduction Based on Classical Mechanics, Cambridge University Press, 2006, with permission.)”
Diagram by Edward Ott, Scholarpedia:
Figure 1: (a) Double well potential V(x) , and (b) the resulting basins of attraction.
Joanna Macy, Mutual Causality in Buddhism and General Systems Theory: The Dharma of Living Systems (SUNY Press, 1991)
Joanna Macy on systems theory/Buddhist philosophy/deep ecology (from her website, not this particular book):
“The greatest revolution of our time is in the way we see the world. The mechanistic paradigm underlying the Industrial Growth Society gives way to the realization that we belong to a living, self-organizing cosmos. General systems theory, emerging from the life sciences, brings fresh evidence to confirm ancient, indigenous teachings: the Earth is alive, mind is pervasive, all beings are our relations. This realization changes everything. It changes our perceptions of who we are and what we need, and how we can trustfully act together for a decent, noble future.”
“a | This is a painting by John Piper that was used as the frontispiece for Waddington’s book Organisers and Genes. In the picture, which is intended to represent the epigenetic landscape, the developmental pathways that could be taken by each cell of the embryo are metaphorically represented by the path taken by water as it flows down the valleys. The water is supposed to be flowing away from the viewer, towards the sea in the distance. But the bifurcations of the valleys look so unnatural that the flow of water actually appears to be towards the viewer. b | A later depiction of the epigenetic landscape. The ball represents a cell, and the bifurcating system of valleys represents the ‘chreodes’ or bundles of trajectories in state space. c | A rare view behind the scenes of Waddington’s landscape. Each valley in the landscape is formed by tension on guy ropes that are attached to complexes of ‘genes’, represented as pegs stuck in the ground. Panel a reproduced with permission from the frontispiece of Ref. 12 © (1940) Cambridge University Press; panels b,c reproduced with permission from Ref. 13© (1957) Geo Allen & Unwin.”
*the permissions quoted above refer to the Nature article, not this post
Figure from http://kallokain.blogspot.com/2010_08_01_archive.html
(Although the top point should really be called “The power to transcend paradigms”)
Leverage points developed by Donella Meadows (1999): “Leverage Points: Places to Intervene in a System”: http://www.sustainer.org/pubs/Leverage_Points.pdf