The hexagon sensemaking canvas (HSC) is a tool in the tradition of the viable systems model, the confluence framework, the cynefin model and the knowledge in formation model.
The HSC can be used in sessions/workshop to work with and /or make sense of storied material, it has proven instrumental in the design process of StoryForms and in the context of consultancy with clients to discuss project scope, goals and outcomes.
Fractals -A fractal is a natural phenomenon or a mathematical set .pdfLAMJM
Fractals -
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that
displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the
replication is exactly the same at every scale, it is called a self-similar pattern. An example of
this is the Menger Sponge.Fractals can also be nearly the same at different levels. This latter
pattern is illustrated in the small magnifications of the Mandelbrot set.Fractals also include the
idea of a detailed pattern that repeats itself.
Fractals are different from other geometric figures because of the way in which they scale.
Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the
new to the old side length) raised to the power of two (the dimension of the space the polygon
resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is
two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere
resides in). But if a fractal\'s one-dimensional lengths are all doubled, the spatial content of the
fractal scales by a power that is not necessarily an integer. This power is called the fractal
dimension of the fractal, and it usually exceeds the fractal\'s topological dimension.
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve
can be conceived of as winding through space differently from an ordinary line, still being a 1-
dimensional line yet having a fractal dimension indicating it also resembles a surface.
Fractal patterns have been modeled extensively, albeit within a range of scales rather than
infinitely, owing to the practical limits of physical time and space. Models may simulate
theoretical fractals or natural phenomena with fractal features. The outputs of the modeling
process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal
analysis. Some specific applications of fractals to technology are listed elsewhere. Images and
other outputs of modeling are normally referred to as being \"fractals\" even if they do not have
strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal
image that does not exhibit any fractal properties. Also, these may include calculation or display
artifacts which are not characteristics of true fractals.
Modeled fractals may be sounds,digital images, electrochemical patterns, circadian rhythms,etc.
Fractal patterns have been reconstructed in physical 3-dimensional spaceand virtually, often
called \"in silico\" modeling.Models of fractals are generally created using fractal-generating
software that implements techniques such as those outlined above.As one illustration, trees,
ferns, cells of the nervous system,blood and lung vasculature, and other branching patterns in
nature can be modeled on a computer by using recursive algorithms and L-systems
techniques.The recursive nature o.
The hexagon sensemaking canvas (HSC) is a tool in the tradition of the viable systems model, the confluence framework, the cynefin model and the knowledge in formation model.
The HSC can be used in sessions/workshop to work with and /or make sense of storied material, it has proven instrumental in the design process of StoryForms and in the context of consultancy with clients to discuss project scope, goals and outcomes.
Fractals -A fractal is a natural phenomenon or a mathematical set .pdfLAMJM
Fractals -
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that
displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the
replication is exactly the same at every scale, it is called a self-similar pattern. An example of
this is the Menger Sponge.Fractals can also be nearly the same at different levels. This latter
pattern is illustrated in the small magnifications of the Mandelbrot set.Fractals also include the
idea of a detailed pattern that repeats itself.
Fractals are different from other geometric figures because of the way in which they scale.
Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the
new to the old side length) raised to the power of two (the dimension of the space the polygon
resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is
two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere
resides in). But if a fractal\'s one-dimensional lengths are all doubled, the spatial content of the
fractal scales by a power that is not necessarily an integer. This power is called the fractal
dimension of the fractal, and it usually exceeds the fractal\'s topological dimension.
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve
can be conceived of as winding through space differently from an ordinary line, still being a 1-
dimensional line yet having a fractal dimension indicating it also resembles a surface.
Fractal patterns have been modeled extensively, albeit within a range of scales rather than
infinitely, owing to the practical limits of physical time and space. Models may simulate
theoretical fractals or natural phenomena with fractal features. The outputs of the modeling
process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal
analysis. Some specific applications of fractals to technology are listed elsewhere. Images and
other outputs of modeling are normally referred to as being \"fractals\" even if they do not have
strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal
image that does not exhibit any fractal properties. Also, these may include calculation or display
artifacts which are not characteristics of true fractals.
Modeled fractals may be sounds,digital images, electrochemical patterns, circadian rhythms,etc.
Fractal patterns have been reconstructed in physical 3-dimensional spaceand virtually, often
called \"in silico\" modeling.Models of fractals are generally created using fractal-generating
software that implements techniques such as those outlined above.As one illustration, trees,
ferns, cells of the nervous system,blood and lung vasculature, and other branching patterns in
nature can be modeled on a computer by using recursive algorithms and L-systems
techniques.The recursive nature o.
This session is from the COMO 2013 Preconference presented by Beth Thornton, University of Georgia. The full PPT is provided here on SlideShare; to follow along with the audio, visit this link: https://valdosta.sharestream.net/ssdcms/i.do?u=7cc2f4ba24014d3
A long conference and a workshop that I gave (with Paul Girard) at the University of Coimbra in the framework of the project "The Importance of Being Digital". The theme of the conference was how digital methods help overcome several classic binary oppositions of traditional social sciences.
This session is from the COMO 2013 Preconference presented by Beth Thornton, University of Georgia. The full PPT is provided here on SlideShare; to follow along with the audio, visit this link: https://valdosta.sharestream.net/ssdcms/i.do?u=7cc2f4ba24014d3
A long conference and a workshop that I gave (with Paul Girard) at the University of Coimbra in the framework of the project "The Importance of Being Digital". The theme of the conference was how digital methods help overcome several classic binary oppositions of traditional social sciences.
Ma che freddo fa..aspettando una nevicata frattale!annalf
Nevicata Frattale... analisi del fiocco di Neve di Koch e sue varianti in L-System Fractal e Turtle Language. Gara Migliore Comunicazione Matematica Progetto Matematica & Realtà Uni Perugia 2014
Triangolo di Sierpinski studiato nel gioco della Torre di Hanoi e usato in un videogioco Fractapanic creato dagli studenti.
Vincitore premio Menzione speciale per la Migliore comunicazione Matematica alla gara Matematica & Realtà Uni perugia 2014
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2. What are Fractals?
Fractal definition from MathWorld
– A fractal is a geometrical object or quantity that
displays self-similarity, in a somewhat technical
sense, on all scales.
– Fractals don’t need to exhibit exactly the same
structure at all scales, but the same "type" of
structures can appear on all scales.
2
3. Koch snowflake
Given an equilateral triangle, we divide each side into three equal
parts, we eliminate the central part and on it we build an equilateral
triangle.
4. Self-Similarity Property of Fractal
Self similarity across scales
– As one zooms in or out the geometry/image has a
similar (sometimes exact) appearance
– Types of self-similarity
Exact self similarity
Approximate self similarity
Statistical self similarity
4
7. Approximate Self-Similarity
Structures that are recognizably similar but not
exactly
– More common type of
self-similarity
– Example: Mandelbrot set
ITEPC 06 - Workshop
on Fractal Creation7
10. Task (in small group)
Build a powerpoint where you describe:
1.What a fractal is
2.A geometrical example
3. Five examples of fractals in the world around us
Which are the most important properties of a fractal?
11. A fractal has the following
features:
1. It has a fine structure at small
scales.
2. It is too irregular to be easily
described in traditional
Euclidean geometric language.
3. It is self-similar (at least
approximately)
4. It has a Hausdorff dimension
which is greater than its
topological dimension
5. It has a simple and recursive
definition.
The term "fractal" was coined by Benoît Mandelbrot
1975 and is derived from the Latin fractus meaning
"broken" or "fractured."
14. [1] M.Barnsley, Fractal Everywhere, AP Professional (1988)
[2] S.Bercia – G.Dragoni – G.Gottardi, Dizionario biografico degli Scienziati,
Zanichelli – Le Scienze (1999) CD-ROM
[3] P.Brandi – R.Ceppitelli – A.Salvadori, Un’introduzione Elementare alla
Modelliz-zazione Matematica, Università degli Studi di Perugia (2000)
[4] P.Brandi - L.Lotti – A.Salvadori, Un'introduzione elementare alla
modellizzazione frattale, Atti Convegno Internazionale Gian Carlo Rota Memorial
Conference, Barisciano (AQ) (2002) 21-34
[5] P.Brandi – A.Salvadori, (a) Sull’istituzione di percorsi multidisciplinari di
approfondimento per il conseguimento di crediti formativi, Atti Convegno Nazio-nale
Mathesis, L’Aquila (1998) 75-78
(b) Un approccio alla modellizzazione matematica: i problemi di ottimizzazione, Atti XX
Convegno Nazionale UMI-CIM, Orvieto (1998)
(c) Una proposta concreta di innovazione didattica tra Scuola ed Università, Atti II
Convegno Nazionale ADT (2000) CD-ROM
I parte, Lettera Matematica PRISTEM, 43 (2002) 17-23
II parte, Lettera Matematica PRISTEM, 44 (2002) 55-61
(e) Modelli Matematici Elementari, I&II, Università degli Studi di Perugia (2002)
Frattali Usati:
Edgar “ Measure,Topology, and Fractal Goemetry” pag 19,30,164
Kevin Lee “ Fractal Attraction”
Gary Flake “ the computational Beauty of nature”pag 109,110
