Usability Research Update Darlene Fichter University of Saskatchewan November 15, 2004.
Lynn S. Fichter Dept Geology/Environmental Science James Madison University 1410h AN: ED23C-03.
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Transcript of Lynn S. Fichter Dept Geology/Environmental Science James Madison University 1410h AN: ED23C-03.
Lynn S. FichterDept Geology/Environmental ScienceJames Madison University
1410hAN: ED23C-03
1. Complex systems are not just simple 1. Complex systems are not just simple systems with a lot more parts.systems with a lot more parts.
PremisesPremises
2. Complex systems have their own 2. Complex systems have their own properties, behaviors, and terminology.properties, behaviors, and terminology.
3. Our students enter our classes with 3. Our students enter our classes with virtually no familiarity with these ideas.virtually no familiarity with these ideas.
Therefore, we must build these Therefore, we must build these concepts for our students from the concepts for our students from the bottom-up – just like for any other new bottom-up – just like for any other new subject.subject.
Bifurcation Bifurcation
Self-similarity Self-similarity
Fractal Fractal
Agents Agents
Self-Self-organized organized criticalitycriticality
AvalanchesAvalanches
Power LawsPower Laws
Strange Strange attractors attractors EmergenceEmergence
The Language of The Language of Complexity Complexity
We can introduce the basic We can introduce the basic concepts in 3 - 5 one-hour concepts in 3 - 5 one-hour classes . . . classes . . .
Teaching Timing ?Teaching Timing ?
. . . I use them in at least 5 different . . . I use them in at least 5 different classes, classes, . . . and, can pull out and develop . . . and, can pull out and develop
specific concepts for specific specific concepts for specific purposes . . . purposes . . .
. . . depending on the depth we want, . . . depending on the depth we want,
All the programs and All the programs and supporting materials are supporting materials are
available on line.available on line.
jmu.edu/geology/ComplexEvolutionarySystems/jmu.edu/geology/ComplexEvolutionarySystems/
Learning Outcomes for understanding chaos theory.
ChaosTheory
Studies why and how the behavior of simple systems—simple algorithms—becomes more complex and unpredictable as the
energy/information the system dissipates increases.Xnext = rX (1-X)
System evolves to equilibrium
The logistic system
A random sampling of logistic curves pulled from Google\images\
logistic curve
ChaosTheory
Studies why and how the behavior of simple systems—simple algorithms—becomes more
complex and unpredictable as the energy/information the system dissipates
increases.Xnext = rX (1-X)
System evolves to equilibrium System evolves to complexity
The logistic system
But, if we push the system
harder
Its behavior evolves into
this.
X next = rX (1-X)
Valueof X
(Populatonsize)
1.0
0.0
0.5
Number of Equation Iterations
r = 2.7
.02.05
.13
.35
.58
.65
.60
.64
.61
.62
X = .02 and r = 2.7 X next = rX (1-X)
X next = (2.7) (.02) (1-.02 = .98)
X next = .0529
Iteration X Value
0 0.0200000
1 0.0529200
2 0.1353226
3 0.3159280
4 0.5835173
5 0.6561671
6 0.6091519
7 0.6428318
8 0.6199175
9 0.6361734
10 0.6249333
11 0.6328575
12 0.6273420
13 0.6312168
14 0.6285118
15 0.6304087
16 0.6290826
17 0.6300117
18 0.6293618
44 0.6296296
45 0.6296296
46 0.6296296
47 0.6296296
48 0.6296296
49 0.6296296
50 0.6296296
.05
.13
.35
.58
.65
.60
.64
.61
.62
X = .02 and r = 2.7 X next = rX (1-X)
X next = (2.7) (.02) (1-.02 = .98)
X next = .0529
.62Equilibrium state
All these systems can be modeled in a All these systems can be modeled in a computer, in class, in real time.computer, in class, in real time.
20 generations
But, what about these irregularities?Are they just meaningless noise, or do they mean something?
r = 2.7
r = 2.9
r = 3.0
r = 3.1
r = 3.5
r = 3.7
r = 4.0
r = 4.1
r = 2.7r = 2.9
X = .629 X = .655
r Value
PopulationSize = X
This axis was a time series, but becomes . . .
Converting a Time Series Diagram into a Converting a Time Series Diagram into a Bifurcation DiagramBifurcation Diagram
r = 3.3 r = 3.5X = .48 & .82 X = .50, .87, .38, .82
split
split
split
r = 3.8
0.877682831619863 0.407951579058487 0.917802935168261 0.286674687986186 0.777070782765993 0.658280769082272 0.854799352927153 0.471646192817398 0.946945034149357 0.190912518507075 0.58696672938057
0.921259794327218 0.275652705596884 0.758739507677205 0.695604695234438 0.804607452168521 0.597414340316927 0.913939695942348 0.298884926867995 0.796300363964611 0.616383158394868
Bifurcation diagram showing behavior of system at all values
of r
2.5 2.9 3.0 3.3
GreatStability at
1 value
IncreasingInstability
Vibrating so hardIt flies apart
Return tostability, but with
2 stable points
L.P. 11 - Change is always accompanied by increasing instability
Properties of Complex Evolutionary Systems
Sensitive Dependenceon Initial Conditions:
Xnext
r = 4.000001
r = 4.000002
Universality
These two runs differ by a millionth of an ‘r’
Complex SystemsTheory
ChaosTheory
Is imbedded within . . .
Complex SystemsTheory
. . . studies how systems with many “agents” that are already at high
energy/information dissipation interact and behave.
ChaosTheory
Agent:the individual units that are
interacting, like . . .
Agents
Agents = units of friction along a
fault zone
Agents = sand
grains in a
migrating ripple
Complex SystemsTheory
Complex systems theory studies how systems with many “agents” that are already at high energy/information dissipation interact and behave.
ChaosTheory
How does complex system theory say the
agents behave?The central dogma is The central dogma is complex systems are complex systems are
Self-OrganizingSelf-Organizing
Self-Organized CriticalityCellular
Automata
BoidsOscillatin
gReactions
Cellular Automata and Self Organization
Survival Rules – 2/3 a live cell survives to the next generation if at least 2 but no more than three of the surrounding 8 cells are alive. Less than 2 and it dies of loneliness; more than 3 and it dies of over crowding.-Birth Rules – 3/3 a dead cells comes alive the next generation if 3, any 3, of the surrounding 8 cells are also alive.
Local Rules/Global Behavior
1 2 3
4
567
8
1 2 3
4
567
8 ?
jmu.edu/geology/ComplexEvolutionarySystems/