Juegos topológicos

Sierpinski Carpet Project

LOGO-sierpinski-carpet-project2

La alfombra de Sierpinski más grande del mundo construida por miles de niños (Spanish).

La catifa de Sierpinski més gran del món construïda per milers de nens (Catalan).

The largest Sierpinski carpet in the world, built by thousands of children (English).

Le plus grand tapis de Sierpinski au monde construit par des milliers d’enfants (French).

Der größte Sierpinski Teppich in der Welt, von tausenden Kindern gebaut (German).

Cel mai mare covor Sierpinski din lume, construit de mii de copii (Romanian).

Největší Sierpinski koberec, který postavily tisíce dětí (Czech).

Największy na świecie dywan Sierpińskiego, wykonany przez dzieci (Polish).

세상에서 가장 큰 시에르핀스키 카펫은 수천 명의 어린이들에 의해서 만들어졌다 (Korean).

A világ legnagyobb, több ezer gyermek által készített Sierpinski szőnyege (Hungarian).

Tuhansien lasten rakentama maailman suurin Sierpinski matto. (Finnish)

(more languages of participating countries are coming)

 


 Ver esta página en Español.

Registration available until October 31st, 2014

(to construct carpets before December 21st, 2014).

List of participants

Captura de pantalla 2014-09-10 18.36.42

Support the Sierpinski Carpet Project by clicking “I like” our Facebook page.

Sponsor some NGOs educational center.  These NGOs will receive free advertising through our project.


 

LATEST NEWS!

The Sierpinski Carpet project enters into the eTwinning community.

Alt ImageThe Sierpinski Carpet project will be available as an european eTwinning project, on September 22th, 2014. Please contact to Dolores Jiménez Cárdenas.

 The European Research Night: September  26th, 2014

The 5th iteration of the Sierpinski carpet will have a side of 4,83 meters. It will be mounted in the Researchers Night, a divulgative event organized by the Fundación Descubre and  OTRI of the University of Almería, on September 26th, 2014.

Parallel, a carpet will be mounted on the Researchers’ Night in Hungary.

The 6th iteration will be real!

We have already booked the 64 places of the 6th iteration. This huge fractal of side almost 15 meters, will be mounted in Cosmocaixa, Barcelona, next October 4, 2014, during the Science on Stage 2014. Below you can see a montage picture of how it will look like.

simulacion-alfombra-COSMOCAIXA5

A simulated Sierpinski carpet of  side 14,58 meters, in Cosmocaixa. (Montage on a picture by the architect Jordi Bernadó)

Each place of the carpet corresponds to a center of our LIST OF PARTICIPANTS.

Simulación de la sexta iteración de la Alfombra de Sierpinski, con la colaboración de 64 centros educativos.

Simulation of the 6th iteration of the Sierpinski Carpet, with 64 carpets from educational centers around the world.


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).

The Sierpinski Carpet project is a collective activity among children from 3 to 12 years old around the world. We want to build a giant geometric fractal, known as Sierpinski Carpet,  with coloured squared stickers. This fractal was described by Waclaw Sierpinski in 1916 (but it was previously discovered by one of his PhD students, 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.

Download the flyer of this activity in Spanish, English, French.

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 etc.. preferably with children between 3 and 12 years (exceptionally until 16).

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 by ordinary mail the carpet to Almería (Spain) when required, for its public exhibition in Barcelona, and other cities.

 Instructions to build the 4th iteration

After filing the registration form, please follow the following steps:

STEP 1: Preparation of the material

The responsible for the activity receives 4096 stikers and 2 templates.

Marks a flap above (to able gluing for the 3th iteration) on the templates (if they are not marked) and makes:

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

(This flap will be already in templates received after September 4th, 2014).

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 3th iterationn

Each group of 8 children make 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 3th iteration with purple corners.

2014-09-03 13.55.00

3th 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;
  2. if even, the model with green corners.

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 this website, at least one photo with all participating children, and in the album of our Facebook page.


 

Organizing team

The Sierpinski Carpet Project originated in the project “Juegos y joyas fractales” (fractal games and jewelry) presented in Science on Stage 2014, to be held next October 3rd to 5th, in  CosmoCaixa, Barcelona. This project is mainly 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

  • Departament of Mathematics, University of Almería.
  • Escuela politécnica Superior y Facultad de Ciencias Experimentales, Universidad de Almería.
  • OTRI, Universidad de Almería.
  • SAEM Thales, Almería.

Some impact on Media, blogs and social networks (in Spanish)

Entrevista en Abierto al atardecer, de Interalmería TV (3 de junio de 2014).

Una alfombra para aprender matemáticas” en el Ideal de Almería, el 16 de junio de 2014.

Lección de matemáticas“, noticia distribuida por la delegación de gobierno de la Jjunta de Andalucía, el 26 de junio de 2014.

La alfombra de Sierpinski y los fractales“, en mi Aula Específica, el 12 de junio de 2014.

Construyendo fractales“, en el blog infantil Goya, el 31 de mayo de 2014.

Proyecto alfombra de Sierpinski“, en la Sociedad Castellano Manchega de Profesores de Matemáticas, el 2 de julio de 2014.

Fractales: el concepto matemático que se describió mirando al mar @Claragrima en Cienciaexplora, el 18 de agosto de 2014.

Recomendado en el Boletín de la Sociedad Matemática Española, el 16 de junio de 2014.

Recent posts about the Sierpinski Carpet:

To infinity… and beyond, by Virginia Hughes, August 12, 2014.

Posts by John Baez in the AMS Blogs

http://blogs.ams.org/visualinsight/2014/07/01/sierpinski-carpet/

http://blogs.ams.org/visualinsight/2014/08/14/733-honeycomb-meets-plane-at-infinity/


 

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

 

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