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Non-Random vs Random -
Order out of Chaos

A Working Analogy for
Natural Selection

Created by Doug Fraser
Timiskaming District Secondary School, Ontario, Canada




Natural Selection
 NEW ARTICLE: Common Misconceptions about Natural Selection. Go to our Evolution Introduction page, scroll down to bottom of page for "A Few Very Common Misconceptions" and a link to the excellent article that exposes a number of widely held misconceptions, with clues for correcting them (June 2009).
For several STEM Applications of Natural Selection


This activity provides an excellent introduction to the concept of biological complexity while at the same time demystifying and debunking Paley's argument that a complex "watch" is compelling evidence requiring a (complex) "watchmaker" (designer/creator). It employs an elegant, simple mathematical exercise to demonstrate this. It involves a randomizing component (a die), and a simple mathematical rule (the non-random component), resulting in the repeated plotting of points. Repeated cycles eventually produce an orderly pattern.


Simple non-random rules, acting on random events can easily produce complex, seemingly "designed" patterns.


Natural selection is a process of non-random events (selection) acting on random events (mutations), resulting in the production of complex systems (new species).


   Students will....

1. Recognize examples of random, chaotic, events.
2. Recognize examples of non-random, orderly events
3. Recognize examples of the results of the interaction of random and non-random processes, as orderly, complex, patterned systems.
4. Recognize that natural selection, as an example of such an interaction, can produce complex changes in living organisms (new species): micro-evolution.
5. Recognize that when selected features accumulate over time, new and modified kinds of structures and species can arise (cumulative selection).
6. Recognize that the accumulation of new species from ongoing selection over time can produce new groups that we recognize in the hierarchy of our modern classification (genera, families, orders, etc.), a process of cumulative speciation, or macro-evolution.


For each team (of 2-4 students):
sheet of blank paper - one die
- ruler - pen or pencil

Living on the Edge: Order, Chaos & Complexity (5 page packet for each student/team)

Slide or Overhead transparency of the Sierpinski Gasket, the fractal design produced in the activity."Chaos Game" interactive computer program (see suggestions below under Resources). Take a look at different versions; Work with Jeff Sprague's Chaos Plotter.

Living on the Edge...for the teacher:..(5 page PDF version of this lesson)



Depending on whether the computer routine is used or not...
Without the computer : could be all or most of 45 minute period.
With the computer: probably no more than 20-30 minutes.
STUDENT HANDOUTS Living on the Edge: Order, Chaos & Complexity (5 pages): Background info, questions for discussion, activity directions. Available in PDF format (click on title)











This lesson should be a critical part of any presentation of natural selection. It could be done as part of a dramatic introduction to natural selection, anticipating possible (popular) doubts about complex or orderly systems being able to arise from random events. This also provides an opportunity to emphasize the NON-random element of SELECTION which is integral to the process.

Alternatively, this lesson could be used following one of the classroom activities that models natural selection (see the several examples on this site). In this way, it could provide a powerful answer to objections students may have heard about the creative powers of natural selection. If students don't raise this challenge, then the teacher should bring it out as a popular criticism, based on a popular misconception and a misunderstanding of the process.

Be sure you have all needed materials for each team, and sufficient copies of the 4-page handout. If you plan to demonstrate (or have students use) one of the computer simulations of the Chaos Game,  be sure it's ready to go and be displayed to the entire class. Otherwise, have the "Sierpinski Gasket" fractal diagram ready to display on your overhead or projector.

THE CHAOS GAME: Graphically presents the multiple cycles of random events interacting with a simple rule, producing the complex fractal pattern called the Sierpinski Gasket.

To show students how to do the Chaos Game, show them the short YouTube clip showing how the plotting is done, and this other clip showing an accelerated view of the fractals building. In addition to this, there is a similar interaction (on the CD) that produces the fractal pattern of a fern frond. Click here for details of the process.

If possible, have students work with Jeff Sprague's Chaos Plotter. Notice that there are four sliders that control parameters (pictured on the left):
1. Polygon: 3 to 12 sides
2. Radius: 5 positions from 1/4 to 3/4
3. Points Plotted: 12 levels, from 10, 500, 5K - 50K (in 5K increments)
4. Speed: (slow - medium - fast)

A good starting/demo combination could be: Polygon 3 (triangle); Radius 1/2; Points 10K; Speed Med. Press START.
There are also 5 Demo runs with pre-set parameters you could try.

Another aspect of natural selection is that the changes are cumulative. This is apparent as points accumulate in the Chaos Game, eventually producing recognizable patterns. Cumulative selection (another often-overlooked but critical aspect of the natural selection process) is also illustrated in the simulation of a monkey typing a Shakespeare quote from Hamlet: "Methinks it is like a weasel", a supposedly random process in which hits that fit survive (stay) and accumulate, until the entire phrase has been typed.

The educational impression of this routine and the basic Chaos Game alone are critically important. Critics of natural selection often mischaracterize the process as totally random, and that the chances of a monkey randomly typing keys coming up with "Methinks it is like a weasel" is so unlikely as to be virtually impossible. But they forget the accumulative nature of natural selection, where little changes that fit or are functional are retained. This lesson makes clear that non-random processes of selection and accumulation make random changes (mutations) that produce a functional change a virtual certainty over a fairly short time. You might also want to consider doing another ENSI lesson that focuses on the cumulative nature of natural selection: A Cumulative Process.




1. Briefly provide a logical context for the lesson, and introduce it.

2. Hand out the lesson (one per team, to be read aloud within each team, or enough for everyone to read quietly).

3. After the teams have a chance to interact on the first set of questions (1-6), give one person per team a turn at sharing team responses with the class in a class-wide discussion.

4. Repeat step 3 with each subsequent set of questions (7-10, 11-14). You might find it works better to allow teams to go through all 14 questions in one sweep, THEN engage the class in sharing their answers.

5. Go on to Part II: Complexity, and the "Chaos Game". Depending on your class, you might want to demonstrate how to plot each point (die, measure, make dot, etc.). The YouTube video showing how the plotting is done can do this nicely.

6. After the class has done a few dozen cycles (or less, if time is short),  with no discernable pattern, do one of the following:
a. project the Chaos Game on the screen (for the whole class to see), and RUN the program, slowly at first, then click on faster speeds. Repeat a few times, each time letting a different student place the initial dot.
b. project the Sierpinski Gasket fractal diagram on the overhead, and point out that this is the result of many hundreds of cycles of what they've been doing. Ask if any team can see the beginning of that pattern in their individual efforts so far.

7. Carry out a class discussion (items #1-25), or allow students to do this within their teams, followed by class sharing at least a sampling of the questions. Allow some time for reflection and conclusions about what they've learned from the lesson.


1. Provide unlabeled examples of various events and objects, and ask students to identify which are examples of chaos (random events or randomly produced objects), which are non-random events/objects, and which are the products of both random and non-random elements.

2. Ask students to explain how natural selection is like the Chaos Game (e.g. which element is random, which element is non-random, and how the product is like the fractal product of the Chaos Game).






1. As a further analogy to natural selection, one which also emphasizes the cumulative nature of this process, take a look at "Natural Selection... a Cumulative process: It's in the Cards" on this site. It's taken directly from an article in The American Biology Teacher by Werner Heim, in which students select a sequence of playing cards two different ways: one cumulative, the other non-cumulative. The chaos game does a great job showing how a combination of random and non-random elements can create order. However, the physical engagement with the cards, and the direct comparison, provides a real sense of the statistical probabilities involved, and may even be more compelling. This is especially true for those who have heard and believed the old anti-evolution argument and the misplaced appeal to intelligent design.

2. To reinforce the concept the the combination of non-random with random events together producing complex designs, along with the concept of cumulative selection, share the "Methinks it is like a weasel" demonstration. Try entering other target phrases, like "Make a human being." And another very interesting variation on this theme (promoted in Richard Dawkins' The Blind Watchmaker," is the Biomorphs interactive (see References below).

3. Another topic which strongly indicates that life has NOT developed by intelligent design is the study of pseudogenes (non functional DNA sequences that are nearly identical to certain functional genes). In fact, this is an excellent opportunity to give your students a chance to see the power of MILEs (Multiple Independent Lines of Evidence). Take a look at our Pseudogene Suite, and consider doing at least the first two lessons there: Lesson A: Why Do We Need Vitamin C In Our Diet?, and Lesson B: What Can Pseudogenes Tell Us About Common Ancestry? These are based on the existence of a pseudogene in humans that is very similar to the gene that enables many other animals to make vitamin C. The lessons show how common ancestry between primates and other mammals is the most likely explanation for that striking similarity.

4. In addition, we would encourage you to extend the unit on natural selection by addressing, at some point, the concept of cumulative speciation and how this results in the phenomenon often called macro-evolution. There seems to be a growing acceptance for natural selection at the micro-evolution level (within a species) amongst creationists, but they still insist that there is "no-evidence" for macro-evolution, so we feel that the mechanism and evidence for this continuum should be clearly presented. See our Intro to Evolution page, in the section on What Evolution IS, and click on the Macroevolution Diagram which can be used to show this (along with directions on its use). You could also use the similar diagram in the NAS book on Teaching About Evolution and the Nature of Science (page 32). Partly for its historical significance, you should also show Darwin's Tree, also accessible from the What Evolution IS section.

Also, Take a look at the handy summary: "Comparing Evolution Mechanisms" near the bottom of that same "Introduction to Evolution" page. Darwin's and Lamarck's essential elements are listed and compared, and a few common misconceptions are clarified. Scroll down to download the PDF file of this information.

5. For further experience with macroevolution, consider using at least one of the following lessons:
Classroom Cladogram of Vertebrate Evolution <http://www.indiana.edu/~ensiweb/lessons/c.bigcla.html>
Hominoid Cranial Comparisons (skulls lab) <http://www.indiana.edu/~ensiweb/lessons/hom.cran.html>
Becoming Whales lesson <http://www.indiana.edu/~ensiweb/lessons/whale.ev.html>.
In each of these, examples, traits are seen accumulating in fossils over time, clearly showing gradual changes in the mosaic patterns of those traits.

6. Finally, you should also take this opportunity to present a sampling of the many transitional forms in the fossil record, something creationists persist in denying, in spite of the abundance of examples. We have a nice condensed version of Kathleen Hunt's treatment of transitional fossils (from her Talk Origins paper). <www.indiana.edu/~ensiweb/lessons/c.bkgrnd.html>. It's called the "Background" and is also accessible from the Classroom Cladogram lesson.


Chaos Game:
http://webserv.jcu.edu/math//vignettes/chaosgame.htm Shows stages during development and variations,  and math behind it
http://commons.wikimedia.org/wiki/File:Sierpinski_chaos_animated.gf Same - stages change in place
https://www.khanacademy.org/computer-programming/the-chaos-game-sierpinski-triangle-generator/2407640941 Excellent: Animated (on right), and short program and var.
https://www.youtube.com/watch?v=MBhx4XXJOH8 Demo of doing Chaos Game: YouTube, good
https://www.youtube.com/watch?v=droTYSmSGHg Demo graphic of plotting points, accelerates
http://www.wildlizardranch.com/chaosGame/ This is Chaos Plotter:
Written in Javascript by Jeff Sprague, a former student of the ENSI webmaster. User can select desired polygon shape, and adjust 4 different parameters.

Methinks it is like a weasel:
http://evoinfo.org/weasel/ [includes totally random process, too] Click on Simulation tab, enter phrase, like "MAKE A
HUMAN BEING" etc. Excellent

Another online interactive version:
http://antievolution.org/cs/dawkins_weasel See Program Control: Click on Run [no visual of totally random events]

http://cs.lmu.edu/~ray/notes/biomorphs/ ORhttp://www.emergentmind.com/biomorphs
User can change parameters. This interactive program is based on Dawkins' The Blind Watchmaker.

Dawkins, Richard. The Blind Watchmaker. 1987. Norton. An excellent read, highly recommended before you present the Chaos Game.

ENSI Mini-Lesson: Natural Selection... a Cumulative Process: It's in the Cardshttp://www.indiana.edu/~ensiweb/lessons/ns.cum.l.html

ENSI Lesson: Pseudogene Lesson A: Why Do We Need Vitamin C in Our Diet? http://www.indiana.edu/~ensiweb/lessons/psa.html


Some of the ideas in this lesson may have been adapted from earlier, unacknowledged sources without our knowledge. If the reader believes this to be the case, please let us know, and appropriate corrections will be made. Thanks.

The original concept and CD for this lesson came from Doug Fraser, a biology/environmental science teacher and biology text co-author Matthew Allen in Ontario, Canada.
With the kind permission of the author, present Chaos lesson was adapted to the ENSI format by Larry Flammer, 2/2003.

8/15/2015 Many changes made by webmaster, reflecting unavailability of the CD by Fraser and Allen. In its place, an interactive Chaos Plotter was kindly developed and donated by Jeff Sprague, former student of the ENSI webmaster, and added to the lesson. There are also now several online interactive versions of the Chaos Game from which to choose.


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