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African Unit 3

Practical Fractal African Algorithms

Name: Penelope Stickney

College: Kankakee Community College

Discipline: Humanities

Module Title: “Practical Fractal African Algorithms”

Narrative Description of the Module: Fractal structure and design is not a new, computer-generated concept but one historically represented in indigenous cultures. This module explores fractal designs found in African villages and the strip-woven cloth patterns of the Ewe people of Ghana and Togo. Application of the woven cloth includes a study of symbols, color, and messages.

Project outcome: Within the curriculum, fractal experiments are applied to other complex African designs including ancient African sculpture. Contemporary examples include fractal design in hair braiding and demonstrate pattern continuity in modern African architecture.

Educational Objectives of the Module
  1. Interpret cultural and geographical history of the Asante people of Ghana
  2. Learn the use of similar patterns, or fractals, as found in traditional African settlements
  3. Recognize the application of fractals in African rhythms and color in Kente cloth designs
  4. Make application to the symbols and images found in historical records and coded language
  5. Realize and apply the significance of symbolism, color, and design as cultural proverbs

Detailed outline of main themes (with accompanying content notes) to be included in the Lectures/Discussions Used to Implement the Module
  1. Week One
    1. Identify geography and history of the Ashanti people
      1. Continental transmigration
      2. The strength of the Ashanti nation
      3. Film (On Demand) The Ashanti Kingdom (14 min.)
    2. Documentary (On Demand) of Ashanti Kingdom (59 min.)
    3. Quiz: History, Culture, Transmigration
  2. Week Two
    1. Garments made from woven cloth, known as Kente, reflect and identify the Ashanti culture.
      1. Color identification and interpretation
      2. Adinkra symbols and proverbial statements
    2. Film content support
    3. Homework: coloring page and personal reflection
      1. Select an Adrinka design print
      2. Use colored pencils (or crayons) to apply color
      3. Reflect on color selection and design; create a reflective proverb
      4. Prepare to explain design, color, and proverb through in-class discussion
  3. Week Three
    1. Introduction of fractals and definition of algorithms
    2. Film by Eglash, "The Fractals at the Heart of African Designs" (16.57)
    3. Kente cloth weaving, contruction, and use in clothing
    4. Introductory Film "Algorithm Africa" (3.06)
    5. Class design weaving project
    6. Extra Credit application:
      1. "Wrapped in Pride" computer-designed Kente cloth algorithm
      2. Create algorithm for medical use as suggested by Ysterplaant Medical Supplies
      3. Additional opportunities for computer-aided algorithmic ideas
Listing of Audio-Visuals Used to Implement the Module (provide electronic links to sites where they can be accessed)
  1. The Ashanti Kingdom (Ghana)
    1. The Akan peoples who made up the Ashanti kingdom are the best-known ethnic group in Ghana, comprising around 2 million of the country’s 12 million inhabitants. All of the Ashanti kings belong to the Oyoko Dako clan, the clan of chieftains; they are the ones who have created and strengthened the Ashanti nation. This program shows the Ashanti kingdom: it explains the strict hierarchical organization of the village, the importance of the characteristic kente garment, the naming of children, the Ashanti religious beliefs, the importance of traditional values and traditional festivals, and the protocol surrounding the paramount chief of the Ashanti. (14 minutes)
  2. Wrapped in Pride: The Story of Kente in America
    1. America Once reserved for African royalty, kente cloth has become a familiar pattern in American culture. Narrated by Tony Award-winning actress Ann Duquesnay, this program traces how kente cloth crossed the Atlantic from the West African Republic of Ghana at the beginning of the civil rights movement to literally become part of the fabric of American life. Film footage shows Ashanti and Ewe weavers making kente, while several scholars and experts discuss the cultural and political significance of this distinctive cloth. (27 minutes)
  3. The 300 Year Old Asante Kingdom (DOCUMENTARY)
  4. Akan People
    1. The Akan ( pronunciation ; /əˈkæn/) are a nation and indigenous ethnic group residing on the Gulf of Guinea in the southern regions of the Gold Coast region in what are today the republics of Ghana and the Ivory Coast in West Africa. This is a detailed account which includes a complete bibliography. Akans are the largest ethnic group in both countries and have a population of roughly 20 million people. The Akan language (also known as Twi–Fante) is a group of dialects within the Kwa branch of the Niger-Congo language family. Also included under the term "Akan" are the Bia languages (in which case it is common to speak of "Akan languages", as a group of languages).
  5. The Fractals at the Heart of African Designs
    1. Ron Eglash is an ethno-mathematician: he studies the way math and cultures intersect. He has shown that many aspects of African design — in architecture, art, even hair braiding — are based on perfect fractal patterns. Eglash states that the African “heritage is about mathematics and not just about singing and dancing.” TEDGlobal2007 (16:57)
  6. Introduction to Kente Weaving in Ghana
  7. Men's and Women's Weaving in Africa:Burkina Faso, Ghana, Nigeria
    1. The art form continues in West Africa and this video explains the process performed by both the narrow-band men's weaving and broad-loom women's weaving in Burkina Faso, Ghana, and Nigeria.
  8. What do Kente Designs Mean?
Student Readings (links to sites where readings can be accessed electronically or by purchase)
  1. Achberger, Jessica. "Kente: Not Just any Old Cloth." The Ultimate History Project. The site identifies Ashanti history, cloth used in trade, and identification of colors used in the designs.
  2. Algorithm Africa. African leaders solve complex problems and convert their aspirations to action through growth opportunities and patterns for success by focusing on identifying, simplifying, changing and advancing business, industry, government and society in Africa.
  3. Dr. Y. "Kente Cloth an Asanti Tradition Dating Centuries Back." Published Aug 15, 2013. "Kente is an Akan royal and sacred cloth worn only in times of extreme importance and is the cloth of kings and nobility, before finding its way into bags, and scarves sold around the globe nowadays. In Akan culture, the different colors and intricate patterns used in the weaving do have traditional meanings.” This history of Kente cloth supports a larger blog about African history and heritage through audio and video files. centuries-back/
  4. Eglash, Ron. "African Fractals: Modern Computing and Indigenous Design." Rutgers UP, Fractal geometry fuses mathematics and informational technology and its patterns are surprisingly common in traditional African designs and fundamental to African knowledge systems. African fractals introduce readers to fractal geometry and explores its expressions in African cultures, including architecture, hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, quantitative techniques and symbolic systems. His book is considered a ‘unique contribution to the study of mathematics, African culture, anthropology, and aesthetic design. Website includes a Table of Contents, Links to Sample Images, and purchasing information.
  5. Eglash, Ron. "Learning and Creating Designs with African Fractals." Create your own fractals
  6. "Examining Ghana’s Use of Intellectual Property Law to protect adinkra and kente fabrics." University of Minnesota. Published Apr 27, 2011. This site identifies further content on the use and purpose of adinkra and kente textiles as creatively used and interpreted in Ghana.
  7. "Kente Cloth Computing." Culturally Situated Design Tools: Teaching Math and Computing Through Culture. Web site gives background on origins, interpretation of color and patterns, contemporary computer application.
  8. Kente "Kente Cloth Adinkra Symbols and Meaning." Site explains Kente pattern interpretations and includes a Documentary about how Kente Cloth is woven
  9. "Kente Cloth Weaving in Ewe, Ghana." vittfamily. Published on Jan 30, 2010. Kente cloth weaving in Ewe. Generally woven by men, boys as young as 12 begin to help their fathers with creating these designs.
  10. Leon, Eli. "Models in the Mind: African Prototypes in American Patchwork." Winston-Salem State University: Winston-Salem, 1992. Draws parallels between African fabric motifs and designs found in African American patchwork quilts. Published e-view:
  11. "Wrapped in Pride: Ghanaian Kente and African American Identity." National Museum of African Art. Web site explains the use of strip weaving construction and use in clothing.
Writing/Field/Experiential Assignments Used to Implement the Module
The following are specialized projects designed to support and enhance undergraduate education:
  1. Kente "Kente Cloth Adinkra Symbols and Meaning." Link offers a lesson plan suggestion which uses crayons and a supplied coloring book to identify color choices and patterns.
  2. "Paper Strip Kente Weaving" United Art and Education Original Art Project. Published Apr 29, 2013. Use weaving strips, markers and yarn to make a Kente Cloth wall hanging
  3. "Wrapped in Pride: Ghanaian Kente and African American Identity." National Museum of African Art. Web site description: Design a kente of your own! You will need the Shockwave plugin, and some patience. At over 500K, the shockwave movie will require a few minutes to download. Once downloaded, you can design as many kente cloths as you wish!
  4. Ysterplaant Medical Supplies. "Resuscitation Council of Southern Africa 2015 Algorithms." Site includes 8 examples of medical algorithms distributed as algorithm posters to hospitals and healthcare facilities. These include: CPR for Everyone, Choking, BLS for Healthcare Providers, Advanced Cardiac Arrest, Newborn Resuscitation, Tachycardia Management, Bradycardia Management, Post Cardiac Arrest Care (ROSC).
Student Evaluation/Testing Regarding the Module
Assessment tool: Students create a fractal art work response to the study.

Intended outcomes for the assessment:
  1. Establish design themes of fractals in indigenous village structure
  2. Explain the parallel between African influence and fractal application
  3. Reinforce fractal design as applies to Kente cloth
  4. Indentify symbols and language of Kente cloth design with fractal emphasis
Fractal Test Kente Lesson Plan To teach about Kente cloth
  1. First explain the symbolism behind the different colors of Kente cloth
  2. Next explain and discuss the intentions of the various patterns
  3. Students design and color their kente cloth patterns
  4. Students are encouraged to internalize the meaning of the colors and symbols and relate their project to their own lives
  5. In class discussion, students will show their kente project designs and explain the meanings of the different colors and symbols they have chosen
  6. The student Kente Cloth Art can be displayed in the classroom

Alternatively, there is included a Kente Cloth Coloring Book in the project website. Studnets may select a design, color it, apply a proverb then share their work with the class. For free download:

"Paper Strip Kente Weaving" United Art and Education Original Art Project. Published Apr 29, 2013. Use weaving strips, markers and yarn to make a Kente Cloth wall hanging.

Ysterplaant Medical Supplies. Resuscitation Council of Southern Africa 2015 Algorithms. Site includes 8 examples of medical algorithms distributed as algorithm posters to hospitals and healthcare facilities. These include: CPR for Everyone, Choking, BLS for Healthcare Providers, Advanced Cardiac Arrest, Newborn Resuscitation, Tachycardia Management, Bradycardia Management, Post Cardiac Arrest Care (ROSC).

Resources (Bibliography) Used to Develop-Implement the Module (where feasible provide links to where resources can be accessed electronically)
  1. Christian, Brian and Tom Griffin. Algorithms to Live By: The Computer Science of Human Decisions. Practical, everyday advice which will easily provoke an interest in computer science. From:
  2. Leon, Eli. Models in the Mind: African Prototypes in American Patchwork. Winston-Salem State University: Winston-Salem, 1992. Draws parallels between African fabric motifs and designs found in African American patchwork quilts. Published e-view:
    1. A fascinating exploration of how computer algorithms can be applied to our everyday lives, helping to solve common decision-making problems and illuminate the workings of the human mind.
    2. All our lives are constrained by limited space and time, limits that give rise to a particular set of problems. What should we do, or leave undone, in a day or a lifetime? How much messiness should we accept? What balance of new activities and familiar favorites is the most fulfilling? These may seem like uniquely human quandaries, but they are not: computers, too, face the same constraints, so computer scientists have been grappling with their version of such problems for decades. And the solutions they’ve found have much to teach us.
    3. In a dazzlingly interdisciplinary work, acclaimed author Brian Christian and cognitive scientist Tom Griffiths show how the simple, precise algorithms used by computers can also untangle very human questions. They explain how to have better hunches and when to leave things to chance, how to deal with overwhelming choices and how best to connect with others. From finding a spouse to finding a parking spot, from organizing one’s inbox to understanding the workings of human memory, Algorithms to Live By transforms the wisdom of computer science into strategies for human living.
  3. lbackstrom. The Importance of Algorithms.
    1. The first step towards an understanding of why the study and knowledge of algorithms are so important is to define exactly what we mean by an algorithm. According to the popular algorithms textbook Introduction to Algorithms (Second Edition by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein), "an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values as output." In other words, algorithms are like road maps for accomplishing a given, well-defined task. So, a chunk of code that calculates the terms of the Fibonacci sequence is an implementation of a particular algorithm. Even a simple function for adding two numbers is an algorithm in a sense, albeit a simple one.
    2. Some algorithms, like those that compute the Fibonacci sequences, are intuitive and may be innately embedded into our logical thinking and problem solving skills. However, for most of us, complex algorithms are best studied so we can use them as building blocks for more efficient logical problem solving in the future. In fact, you may be surprised to learn just how many complex algorithms people use every day when they check their e-mail or listen to music on their computers. This article will introduce some basic ideas related to the analysis of algorithms, and then put these into practice with a few examples illustrating why it is important to know about algorithms.
  4. lbackstrom. The Importance of Knowing Algorithms
    1. As a computer scientist, it is important to understand all of these types of algorithms so that one can use them properly. If you are working on an important piece of software, you will likely need to be able to estimate how fast it is going to run. Such an estimate will be less accurate without an understanding of runtime analysis. Furthermore, you need to understand the details of the algorithms involved so that you’ll be able to predict if there are special cases in which the software won’t work quickly, or if it will produce unacceptable results.
  5. lbackstrom. Conclusion
    1. The different algorithms that people study are as varied as the problems that they solve. However, chances are good that the problem you are trying to solve is similar to another problem in some respects. By developing a good understanding of a large range of algorithms, you will be able to choose the right one for a problem and apply it properly.
  6. Kuchling, A.M. Background: Algorithms. (Copyright 2012)
    1. An algorithm specifies a series of steps that perform a particular computation or task. Algorithms were originally born as part of mathematics – the word “algorithm” comes from the Arabic writer Muḥammad ibn Mūsā al-Khwārizmī, – but currently the word is strongly associated with computer science. Throughout this book we’ll examine a number of different algorithms to perform a variety of tasks. Consider: Algorithms resemble recipes. Recipes tell you how to accomplish a task by performing a number of steps.
Studying algorithms is a fundamental part of computer science and Kuchling presents several different characteristics of an algorithm with the following questions:
  1. Does an algorithm actually exist to perform a given task?
  2. If someone proposes an algorithm to solve a task, are we sure that the algorithm works for all possible inputs?
  3. How long does the algorithm take to run? How much memory space does it require?
  4. Once we know it’s possible to solve a problem with an algorithm, a natural question is whether the algorithm is the best possible one. Can the problem be solved more quickly?
Measuring Complexity: Kuchling adds, “It’s obviously most important that an algorithm solves a given problem correctly. How much time an algorithm will take to solve a problem is only slightly less important. All algorithms must terminate eventually, because they wouldn’t be algorithms if they didn’t, but they might run for billions of years before terminating. In order to compare algorithms, we need a way to measure the time required by an algorithm. We need to know how its running time changes in relation to the size of a problem.”
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