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«Silene hifacensis»

Joanbanjo. *Flors d'esclafidora d'Ifac* (CC BY-SA)

Recientemente se ha descubierto en un manuscrito de Heinrich Moritz una localización encriptada de la Silene hifacensis, una planta endémica en peligro de extinción.

A primera vista, el texto parecía una serie de letras y números aleatorios, pero se sabía que contenía información de vital importancia para localizar la planta. Personal especializado (criptógrafos, lingüistas, biólogos, etc.) han estudiado el texto en detalle y han llegado a la conclusión de que estaba codificado utilizando una serie de matrices que habían sido manipuladas de una manera muy particular.

Tras meses de intenso trabajo, el equipo descubrió una pista crucial que les permitió resolver el cifrado.

Matrices

Los técnicos han encontrado la matriz clave siguiente:

\[ C=\left(\begin{array}{lllll}
E & D & P & X & L \\
U & V & R & S & W \\
A & F & H & I & C \\
Y & T & Q & M & N \\
J & B & G & K & O
\end{array}\right)\]

Y han recompuesto la siguiente imagen:

Los técnicos han decidido codificar la siguiente imagen de forma matricial, usando 0 para el negro y 1 para el blanco.

Al mismo tiempo han encontrado las siguientes matrices:

\[ P=\left(\begin{array}{lllll} 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right) \qquad Q=\left(\begin{array}{lllll}
0 & 1 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 1 & 0
\end{array}\right) \qquad R=\left(\begin{array}{lllll}
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 0
\end{array}\right) \]

Investiga

Toma un matriz cualquiera \( M \in \mathbb{M}_{5x5} \). Investiga las siguientes cuestiones:

Cuestión 1

Observa qué ocurre cuando realizas el producto \( P \cdot M \). ¿Qué efecto tiene sobre M? ¿Y si realizas la operación \( P^2 \cdot M \)?

Cuestión 2

Observa qué ocurre cuando realizas el producto \( M \cdot Q \). ¿Qué efecto tiene sobre M?

Cuestión 3

Observa qué ocurre cuando realizas el producto \( R \cdot M \). ¿Qué efecto tiene sobre \( M \)?¿Y si la operación que realizar es \( R \cdot P \cdot M \)? ¿Y \(R^5 \cdot M\)?

Escribe un informe explicando que efecto producen las matrices P, Q, y R sobre una matriz cualquiera \[ M=\left(\begin{array}{lllll}
a_{11} & a_{12} & a_{13} & a_{14} & a_{15} \\
a_{21} & a_{22} & a_{23} & a_{24} & a_{25} \\
a_{31} & a_{32} & a_{33} & a_{34} & a_{35} \\
a_{41} & a_{42} & a_{43} & a_{44} & a_{45} \\
a_{51} & a_{52} & a_{53} & a_{54} & a_{55}
\end{array}\right) \]

Máscaras

Una de las suposiciones que han hecho los técnicos ha sido que la matriz M es la obtenida al codificar la máscara con 0 (blanco), 1 (negro), 2 (rojo) y 3 (azul).

Observa las siguientes imágenes y averigua qué operación de matrices la genera.

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0 1 2 3 4 5 6 7 8 9 10 11 12

Su navegador no es compatible con esta herramienta.

La «Silene hifacensis» está en...

Alguna de las máscaras anteriores superpuesta sobre la matriz clave deja al descubierto en los elementos en blanco las letras que componen el lugar de la localización de la Silene hifacensis, tras reflejar en un espejo.

¿Sabrías dónde se encuentra?

Utiliza las máscaras en blanco y negro que has encontrado en el juego anterior.

Recuerda:

Escribe la solución en letras mayúsculas, con tildes y sin espacios.

¡Muy bien!

La Silene hifacensis se encuentra en los alrededores de Calpe.

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Su navegador no es compatible con esta herramienta.

Reflexiona

Elija la respuesta correcta.

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Su navegador no es compatible con esta herramienta.

Recursos

Calculadora científica o gráfica.
Geogebra.
Hoja de cálculo.

Productos evaluables

Informe detallado sobre la acción de las matrices P, Q y R.
Resolución de la localización de la Silene hifacensis.

Instrumentos y técnicas de evaluación

Técnicas

Observación directa.
Análisis de desempeño.

Instrumento

Escala de valoración (versión editable (odt - 0,27 MB)/ versión imprimible (pdf - 0,26 MB))

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