Juegos topológicos

Sierpinski Carpet Project

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The Sierpinski Carpet Project is a nonprofit, collective and joint activity among children,  from 3 to 99 years old, around the world. We want to build a giant geometric fractal, known as Sierpinski Carpet,  with coloured squared stickers.


Description of the project

DSC09200

The first carpet was built on May 30th, 2014, in CEIP Francisco de Goya, Almería. In the picture: José L. Rodríguez (left) and David Crespo (right).

This fractal was described by Waclaw Sierpinski in 1916 (but it was previously discovered by one of his PhD student, Stefan Mazurkievicz, in 1913).  It is constructed by dividing a square in 9 others of side 1/3 of the primitive and eliminating the square which occupies the central position, repeating this process in each of the squares that remain, at infinitum. We can see it better with this animated gif (see source):

“Animated Sierpinski carpet” by KarocksOrkav

In each iteration, the number of squares is multiplied by 8 and instead the same side is 1/3 of the above. This produces a geometrical object with a gap of zero area but with infinite perimeter. How many stickers will need in each iteration? What is the area and perimeter of such iterations? and its height? Which iteration could cover our city? What applications has this fractal to? Did you know that there are chips with this design? You can see some calculations in the webpage by  David Crespo.

Objectives

  • To introduce the concept of fractal through a classic example as it is the Sierpinski carpet.
  • To familiarize the student with its construction, based on the self-similarity.
  • To develop the manual and visual work.
  • To highlight the cooperative work, and positive interdependence, as a way of getting a sizeable construction.

Who can participate in this activity?

All schools in the world, hospital schools, cultural associations, individual people, disable children and adults, etc…

What does each center?

  1. Each participating center builds the 4th iteration of the Sierpinski carpet, with 64 children and 64 stickers each, 4096 stickers in total. This material and the templates are included in the registration fee.
  2. (optional) Coordinate with other 7 schools (or classrooms of the same school) to mount the 5th iteration in a public local exhibition.
  3. (recommended) Work in the classroom some supplementary activities.
  4. Send the carpet to Almería (or other ambassadors), by ordinary mail when required, for public exhibition of bigger iterations.

Instructions to build the 4th iteration

After filing the registration form, and follow the payment instructions, please follow the following steps:

STEP 1: Preparation of the material

The responsible for the activity receives 4096 stickers and 2 templates and makes:

  1. 32 copies of the template type P (purple corners);
  2. 32 copies of the template type G (green corners).

STEP 2: Every child makes the 2nd iteration.

Every child gets one copy of these templates (type P or G), together with 32 purple stickers and 32 green stickers and makes one the following 2nd iterations:

20140904_142602

For the 4th iteration we need 32 filled templates with purple corners, and 32 with green corners.

STEP 3:  8 children can form the 3rd iterationn

Each group of 8 children makes the 3rd iteration as shown in the next pictures. The rule is that two squares together must be of diferent colours.

20140904_141718

Position before gluing the 3rd iteration with purple corners.

 

2014-09-03 13.55.00

3rd iteration with purple corners. Students make 4 of these copies with purple corners + 4 copies with green corners.

 

 STEP 4:  Construction of the 4th iteration

8 copies of the 3rd iteration give the 4th iteration of the Sierpinski carpet. You can mount it over the floor, a big table, or over a wall using blu-tack (or similar).

According to the assigned number (see LIST OF PARTICIPANTS), the center chooses one of the two carpets (although this does not matter now with the new instructions):

  1. if odd, follow the the model with purple corners;7. ODD-MODEL modelo de alfombra con número impar con esquinas moradas
  2. if even, the model with green corners.
    6. EVEN-MODEL-modelo de alfombra con número par con esquinas verdes

QUICK GUIDE shows how to mount and disassemble the carpet in order to send it by ordinary mail.

 STEP 5:  Send the carpet by ordinary mail

The carpet disassembled into 8 pieces, and folded as shown in the quick guide, should be sent by ordinary mail to the clossest ambassador or main coordinator when required, to mount 5th, 6th or the huge 7th iteration, in public events before the required date.

STEP 6:  Divulgation

Please, publish some post on your blog or website, local newspaper, etc. talking about your activity as part of the wolrd Sierpinski Carpet Project. Send us some pictures or link to publish them in the page of list of participants, or in our Facebook page.


Registration

Registration available for the 3rd phase. Deadline: January 31st, 2015.

(to construct carpets before March 21st, 2015).

Registration fee: 10 Eur (+shipping costs), for 64 children.

See Payment instructions.


 

List of participants

See the  list of participants, with pictures, videos, links, etc.

Captura de pantalla 2014-10-12 13.00.57

 


 

Organizing team

Director: José L. Rodríguez, University of Almería (jlrodri@ual.es, telf. (+34)617666437)

Co-director: David Crespo Casteleiro (High School responsible) (davidcasteleiro@hotmail.com)

e-Twinning coordinator: Dolores Jiménez Cárdenas, Primary School San Fernando, Almería (lola.jimenez66@gmail.com).

The Sierpinski Carpet Project originated in the project “Juegos y joyas fractales” (fractal games and jewelry) was presented in Science on Stage 2014, held in  October 3rd to 5th, in  CosmoCaixa, Barcelona, winning the 1st prize in Mathematics. This project was organized by José L. Rodríguez (University of Almería, author of this blog), together with David Crespo Casteleiro, Carmen Sánchez Melero (Huercal de Almería), Dolores Jiménez Cárdenas (CEIP San Fernando, Almería),  Lidia García López (IES Francisco Montoya, Las Norias de Daza, El Ejido).

FERIA DE CIENCIAS 137-web

De izd. a dcha.: Lidia, David, Sara, Lola y JL en la Feria de la Ciencia de Sevilla

We would like to thank the colaboration of Mª Teresa Castellón Pérez (CEIP Padre Manjón) and Eufrasio Rigaud (IES Mar Serena, Pulpí) and Jérôme Scherer (Lausanne) for their help preparing and/or translating materials for the Sierpinski Carpet Project, and many other people who is interested and spreading the project around the world.

Colaborating institutions

  • Departamento de Matemáticas, Universidad de Almería
  • Escuela Politécnica Superior y Facultad de Ciencias Experimentales, Universidad de Almería.
  • Vicerrectorado de Internacionalización y Cooperación al Desarrollo, Universidad de Almería.
  • Oficina de Transferencia y Resultados de Investigación, Universidad de Almería.
  • SAEM Thales, Almería / SAEM Thales, Andalucía.
  • Ciencia en Acción, Barcelona.
  • Museo de Almería.
  • Universitat Politécnica de Catalunya.
  • Comité Español de Matemáticas (CEMAT) http://www.ce-mat.org/
  • Mediterranean Institute for the Mathematical Sciences (MIMS)

Sponsors

Benefits of our games are supporting the Sierpinski Carpet Project:


 

Copyright @ 2014 Juegos Topológicos. Universidad de Almería. Todos los derechos reservados.

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