Self

Organization
and
Emergence
Emergence in Graphs
Graphs
Isomorphic graphs
Vertices map to vertices and edges map to
edges such that the relationships between
vertices and edges are preserved.
Consider a fully

connected graph
with 25 randomly
placed vertices
(i.e., K
25
)…
Consider a fully

connected graph
with 25 randomly
placed vertices
(i.e., K
25
)…
But, what if we
care about the
placement of
vertices?
For example,
consider K
25
with
vertices arranged
on a circle…
What do you see?
Arranged
vertices
and
emergent
patterns
Key idea: Systematic circular
arrangement of vertices in a fully
connected graph results in the
visual perception of a collection
of concentric circles formed by
the intersection of the edges.
These circles represent an
emergent property of the graph
(as they are not explicitly
specified in the construction
parameters).
http://www.sacred

destinations.com/italy/venice

san

marco

photos/slides/interior

cc

petunia2323
Spandrels?
Some Questions
1.
Under what circumstances will visual patterns emerge?
2.
What mechanisms exist for detecting emergent patterns?
3.
Are there rules for predicting pattern emergence?
4.
What about reverse

engineering?
5.
Are there any practical ramifications?
Under what circumstances will
visual patterns emerge?
Key factors:
Arrangement of vertices
# of vertices
# of edges
Arrangement of edges
Vertex proximity (i.e., size of graph)
Reminder: this is a matter of visual perception!
K
25
K
24
Odd or even number of vertices…
24 vertices, 138 random
connections (50% of all
possible edges)
24 vertices, 207 random
connections (75% of all
possible edges)
Number of edges…
24 vertices with 4 random
edges per vertex
Arrangement of edges…
24 vertices with 4 regularly
spaced edges per vertex
Vertex proximity
K
25
Vertex proximity
K
25
Vertex proximity
K
25
Vertex proximity
K
25
Vertex proximity
K
101
zoom x 1
Vertex proximity
K
101
zoom x 3
Vertex proximity
K
101
zoom x 5
Vertex proximity
K
101
zoom x 7
Vertex proximity
K
101
zoom x 9
Vertex proximity
K
101
zoom x 19
Vertex proximity
K
101
zoom x 29
Vertex proximity
K
101
zoom x 51
A Simple Cellular Automaton
Imagine a one

dimensional grid of cells with possible states 0 or 1
The state of each cell changes based on its current state and the
state of its two immediate neighbors
There are thus 8 parent combinations: 000, 001, 010,…, 111.
There are 2
8
= 256 possible rule sets
(e.g. 000→0/1, 001→0/1, …, 111→0/1 with child at the center).
All cells change state simultaneously
Successive generations are displayed one under
the other and the resulting pattern is observed.
0
0
1
0
1
1
1
0
1
1
Emergence!
Emergent properties in CA: Cellular automata
illustrate the idea that complex (emergent)
behavior can arise from a simple rule set
http://ourworld.compuserve.com/homepages/DP5/pattern1.htm
http://www.ucmp.berkeley.edu/people/klf/MicroGalleryLarge_files/Radiolarian2.jpg
http://static.open.salon.com/files/zebra

picture1220629421.jpg
“Principle of Computational Equivalence: all processes, whether they are produced
by human effort or occur spontaneously in nature, can be viewed as computations.”
(Wolfram p.715,
A New Kind of Science
)
Crystallization
Self

Assembly
(Pelesko)
http://www.canyonsworldwide.com/crystals/pictures/CrystalCavesRick.jpg
http://upload.wikimedia.org/wikipedia/commons/thumb/7/78/Devils_postpile_NM.jpg/800px

Devils_postpile_NM.jpg
http://upload.wikimedia.org/wikipedia/commons/4/46/Devils_Tower_CROP.jpg
Self

Assembly
(Pelesko)
Diffusion Limited Aggregation
Algorithm
Seed the center of a large, rectangular lattice
Loop
Add particle at boundary of system
Take particle on a random walk until it is adjacent to an occupied position
Add the particle to the aggregate at its current position
Until constraint(s)
http://www.its.caltech.edu/~atomic/snowcrystals/frost/frost.htm
http://www.its.caltech.edu/~atomic/snowcrystals/frost2/frost2.htm
Swarm
Intelligence
Hofstadter,
Gödel, Escher, Bach
, p.358
Swarm: “loosely structured collection of
interacting agents”
(Santa Fe Institute)
An autonomous agent is a system situated
within and a part of an environment that
senses that environment and acts on it,
over time, in pursuit of its own agenda and
so as to effect what it senses in the future.”
(Franklin and Graesser, 1996)
Boids
(Craig Reynolds)
http://www.red3d.com/cwr/boids/
Gravity Waves Over Iowa
Cosmological Emergence
Exploring Motion Demos
Conway's Game of Life (1968)

(cf. Levy)
2D; 2 states/cell (alive/dead); 8 neighbors/cell
Living cell survives if 2 or 3 neighbors are alive
Living cell dies of overcrowding if > 3 living neighbors
Living cell dies of exposure (loneliness) if < 2 neighbors
Cell is "born" if exactly 3 neighbors are alive
Game of Life
Demo
or
http://www.math.com/students/wonders/life/life.html
http://www.indianastandardsresources.org/admin/library/codon_acid.pdf

helix:
–
60
–
60
(3.6 amino acids per 360
turn

獴牡湤猺r
–
135
135
Secondary Structure
Fundamental Concepts of Bioinformatics
: Krane and Raymer
Protein Folding
http://cnx.org/content/m11461/latest/protein_folding.jpg
http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/a/a9/Protein_folding.png&imgrefurl=http
://commons.wikimedia.org/wiki/Image:Protein_folding.png&h=440&w=994&sz=69&tbnid=ZFo3e4RHz0sJ::&tbnh=66&tbnw=149
&prev=/images%3Fq%3Dprotein%2Bfolding%2Bimages&hl=en&usg=__z6Rs6HBySUrszdZoVlm6j7y

G

E=&sa=X&oi=image_result&resnum=2&ct=image&cd=1
http://www.cs.ucl.ac.uk/staff/d.jones/t42morph.html
Protein folding videos:
http://www.youtube.com/watch?v=swEc_sUVz5I
http://www.youtube.com/watch?v=meNEUTn9Atg&feature=related
http://www.youtube.com/watch?v=AlfvWESPyZY&feature=related
Self

Assembly
(Pelesko)
http://www.answers.com/topic/micelle
http://simscience.org/membranes/advanced/essay/micelle.html
Micelles
Self

Assembly
(Pelesko)
Packing parameter = v/(a
0
l
c
) where v is the volume of the hydrocarbon
chain; l
c
is the max effective length that chains can assume; a
0
is the
surface area occupied by the head group in a given structure
Draw a colored equilateral triangle
Repeat indefinitely for every colored triangle
currently in existence
Connect the midpoints of each side to form
four separate triangles
Color the center triangle black
Problem: Construct a Sierpinski Triangle
Algorithm
Create an equilateral triangle with vertices
A
,
B
,
C
Select a random starting point
p
within the triangle
LOOP UNTIL satisfied or bored
generate a random integer
r
from 1 to 3
IF
r
= 1: draw a line from
p
to vertex
A
IF
r
= 2: draw a line from
p
to vertex
B
IF
r
= 3: draw a line from
p
to vertex
C
set
p
= the center of the new line
END LOOP
Sierpinski Triangle Via Randomness
(random processes can generate predictable results)
Sensitivity to Initial Conditions
Consider the 1D CA examined earlier: Note that changing the starting cell states
can result in changes to the final outcome…
For example, consider rule 22 with a random start state versus a start state
consisting of a single white cell (1) surrounded by all black cells (0)…
A New Kind of Science
(Wolfram), pp. 231,235
An Algorithm for Everything?
From Brain Stuff to…
mage source:
http://domino.watson.ibm.com/comm/pr.nsf/pages/rscd.n
eurons_picb.html/$FILE/NeuronsInAColumn1_s.bmp
http://www.brainbasedbusiness.com/uploads/neuron.jpg
http://www.sciencemuseum.org.uk/on

line/brain/images/1

1

8

0

0

0

0

0

0

0

0.jpg
http://www.cirrusimage.com/hymenoptera_Great_Golden_Digger_Wasp.htm
mage source:
http://domino.watson.ibm.com/comm/pr.nsf/pages/rscd.neuro
ns_picb.html/$FILE/NeuronsInAColumn1_s.bmp
mage source: http://www.mabot.com/brain/
10
11
neurons 10
14

10
15
connections
http://www.brainbasedbusiness.com/uploads/neuron.jpg
http://www.chm.bris.ac.uk/webprojects2006/Cowlishaw/300px

Action

potential.png
How does meaning arise from mindless mechanisms?
http://www.russianlegacy.com/catalog/images/matryoshka_traditional/ND50

001.jpg
What’s inside that makes you
conscious/intelligent?
Huse, S. (1993).
The Collapse of Evolution
. BakerBooks: Grand Rapids, MI, p. 53
Presumed Lack of Sufficient Time
Huse, S. (1993).
The Collapse of Evolution
. BakerBooks: Grand Rapids, MI, p. 53
Presumed Lack of Sufficient Time
mechanism?
mechanism?
mechanism?
mechanism?
mechanism?
1.
The Primordium
2.
Making a Non

uniform Universe
3.
The Emergence of Stars
4.
The Periodic Table
5.
Planetary Accretion
6.
Planetary Structure
7.
The Geospheres
8.
The Emergence of Metabolism
9.
Cells
10.
Cells with Organelles
11.
Multi

cellularity
12.
The Neuron
13.
Animalness
14.
Chordateness
15.
Vertebrates
16.
From Fish to Amphibians
17.
Reptiles
18.
Mammals
19.
The Niche
20.
Arboreal Mammals
21.
Primates
22.
The Great Apes
23.
Hominization
24.
Tool making
25.
Language
26.
Agriculture
27.
Technology and Urbanization
28.
Philosophy
29.
The Spirit
Note that even our theories have an emergent character. For example, consider
Morowitz comments (p.8): “Science starts with the mind, both as the perceiver
of sensations and the postulator of constructs… This, of course, presents an
epistemic circle. One starts with the mind as the primitive and goes around the
circle of constructs in an effort to explain mind.”
The Emergence of Everything
(Morowitz, p. 8)
Key Pruning Principles
1.
A given set of (low

level) building blocks can only
go together so many ways based on physical,
chemical, environmental, etc. constraints.
2.
Self

organization is a basic principle of nature
(creating
pockets of order
that buck the trend
toward increasing entropy).
rules
disorder
order
3.
Learning means ordering (arranging).
One example cited in the literature
1
is that even
something as simple as randomly generating the
word “evolution” from the 26 letters of the English
alphabet is prohibitively unlikely.
Probability is (1/26)
9
= 1/26
9
≈ 1 / 5,429,503,700,000
But evolution doesn’t just put random things together!
Presumed Inadequacy of Random Processes
1
Huse, S. (1993).
The Collapse of Evolution
. BakerBooks: Grand Rapids, MI, p. 84
Consider random generation of the string “evol” (probability is
(1/26)
4
=
1 / 456976:
rgvh
lyvn
qxlg
bill
qjit
wjzy
…
yymn
otfo
xkjr
lwyk
epug
ggoq
evol
Target string generated on trial # 149932.
Several other tests resulted in 250561, 520139, and 261924 trials…
Presumed Inadequacy of Random Processes
Human Origins: Alternative Perspective
http://embryo.soad.umich.edu/
Consider the 2
nd
Law of Thermodynamics…
Self

organization: “the study of the way in which systems
made up of simpler elements, governed by simple dynamical
principles, spontaneously develop organization or patterns of
order at a higher level.”
1
Emergence: A scenario in which complex patterns and
behaviors arise from relatively simple collections of rules.
(“The whole is more than the sum of its parts…”) Morowitz
calls emergence “the opposite of reduction.”
2
1
Werbos, P.
Origins: Brain & Self Organization
, p.18
2
Morowitz, H. (2002).
The Emergence of Everything
. Oxford University Press: New York, p.14
If I can write the equations for something is it an
emergent property?
Is emergence real or just perceived?
What is the relationship between determinism
and randomness in self

organizing systems?
How can meaning and purpose emerge in self

organizing systems?
How can God operate through emergence?
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