Anachronic Reliefs by Sattam Aljehani

Anachronic Reliefs INCONGRUOUS TAXONOMES

Wassem Hawary Sattam Aljehani 2013_SPRING_ARCH.565.S1 Teacher: Biayna Bogosian Teacher: Maximiliano Spina Visualization 4: Evolving Media

Outline Introduction - Case studies 1-4 - Introduction to the geometric pattern system. 5-6 - The basic principles of the geometric pattern construction.5-6 - Methods and principles 5-6 2D Geometric Pattern Deformation and Analysis - Regular Pattern 7-8 . Regular pattern of congruent regular polygons. . Covers plane entirely . No overlap.

- Periodic Pattern 8-11 . Patterns with translational symmetry . Overlap pattern.

- Pattern Variation - Non-periodic Pattern 2D TO 3D PATTERN TRANSLATIONS - Principles of the 3d Construction . principles . 2D pattern and 3D forms relation - The Relation to the initial pattern - 3D Geometric patterns

Case Studies Growth 1- I slamic Tilings and Traditional Strapwork.

The Islamic world has a rich heritage of incorporating geometry in the designs that appear on architecture, tiles, and some fabrics. According to Raymond “ Many of these complex patterns or designs can be constructed using“ strapwork method” where circles and squares are transformed into stars and overlapping lattices in order to form a more intricate symmetric pattern”.

Strapwork Method showing constriction from circles to lines to stars to overlapping.

2-

Nonperiodic and Aperiodic Tilings

Many patterns can be constructed using the strapwork method, however, some of the designs which do not repeat in a linear direction may require additional construction techniques which are called nonperiodic . For example, the tilings in the Ottoman Green Mosque in Turky and Mausoleum of I’timad al-Dula in India show decagonal (ten-point) symmetry which in modern times has been discovered in “ quasicrystal structures” .

Moreover, there are some patterns are periodic which have translational symmetry and it only has 2-fold, 3-fold, 4-fold and 6-fold rotationalsymmerty is allowed.

Interlacing, Hierarchy Quasicrystals in Ismalic Architecture Tiling theory studies how one might cover the plane with various shapes. Islamic architecture has developed intricate geometric tailings to decorate some buildings, places and fabric, such as mosques, mausoleums and shrines etc. According to Raymond Tennant who is a professor of Mathmetics in Alhosn University “ The first appearance of these patterns was in 12th Century, and some of these Islamic patterns is called Girih Tilings”.

In addition, Raymond illustrated that “ Recent investigations show that the mathematical understanding of these artisans was much deeper than originally thought”. Furthermore, Studies like these can provide a great opportunity for architects to discover the beauty of Islamic architecture in a mathematical and historical context.

Masjid Jami Yazd Iran 1364-1470 C.E

Itimad al-Dawla Mausoleum in Agra India 1622 C.E

Décor de la médersa d'Abdullah Khan (Boukhara, Ouzbékistan) 1588C.E

Celling of Gunbad-i Uljaytu, Sultaniya, Iran 1304 C.E

Darb-i Imam Shrine, Isfhan, iran 1453 C.E

3-

Medieval Tilings with Girih Tiles

Examples of intricate nonperiodic tilings dating from the 10th to 15th Century AD may be found throughout the world, which are very complex patterns that appear throughout Islamic art and architecture

Darb-i Imam shrine in Isfahan, Iran.

Pattern Deformation and analysis Methods and steps which showing constriction from circles, octagon , lines to stars to overlapping.

A

E

B

C

D

F

G

H

(A) A periodic tiling of the plane with regular octogons. (B) A periodic tiling of the plane with regular octogons, circle center.

(C) regular octogons and circles connact to the octogon vertex, which created the overlapping moments.

(D with the initial vertex. (E) Periodic tiling of the plane with regular octagons, circles, overlapping moments, rotated square 68 째 and arrayed.(F) Connecting each square vertex with another square vertex in order to obtain a rectangular. Arraying the (G) Identifying new parameters from arraying and rotating the rectangular in pattern F. (H) extending the square lines to reach stripes lines.

with the numbers of patterns discovered and the names of the systems experimented.

Identifying new moments

Diagonal stripes pattern

Flower shaped pattern Rotated rectangular

Identifying form

Triming the center cericle

Identifying new moments

Arrayed and Rotated square 68째 Identifying octagon

extending square lines

iterations and 2D moments, and these output could have

Trimmed Star shaped pattern The midpoint of a line segment

Star shaped pattern The midpoint of a line segment

Arrayed and Rotated square Identifying octagon

Identifying new moments between the cells

Identifying new moments

Flower shape pattern The midpoint of a line segment

Arrayed and Rotated square Identifying octagon

Diagonal stripes pattern Identifying new moments

These iterations below came from multi Rotation and overlap processes, which it provides variations of forms in the initial Pattern that can generate new methods of construction

Simple grid

0 iterations

180째 rotation

overlap pattern

1 iterations

Identifying new forms

Identifying new forms

2 iterations

3 iterations

Identifying new forms

Identifying new forms

4 iterations

Identifying new forms

5 iterations

6 iterations

7 iterations

8 iterations

9 iterations

10 iterations

11 iterations

New shapes A1 iterations

A2 iterations

A3 iterations

A5 iterations

A6 iterations

A8 iterations

A9 iterations

A12 iterations

A13 iterations

A10 iterations

A14 iterations

A11 iterations

A15 iterations

by the geometric forms in the pattern and moves along a desired path (possibly rotating as it does so).

Step 1

Perspective view of the pattern

Front view of the pattern Step 2

The second technique, (I) we constructed a rhombus shape from decagram valume , and we constructed congruent triangles between every threevertices, and that in order to create a four sided parallelogram with equal sides, and to prove that the rhombus is symmetric across each of these diagonals (II) and we connected each vertices to the opposite vertices. In (III) we extended the lines until they intersected, so we could deterime the external points (IV), which it would determine the length of the extruded face octahedrons (V)

I

II

(VI) a top view of the pattern after adding a point attractor

V

III

(VII) a top view of the pattern after simplifying it

3D Form after adding a cube to it

simple cylinder shape and in (II,III,IV) we divided to 8 segments. (V) We rotated the bottom face of the octagon 22.5°, and in (VI) we connected the edges of the top face to vertex of the bottom face to create triangular shapes, the center of the triangular shape generates a pentagon shape.

22.5 Degree

0¬

¬

.5

(II)

Simple cylinder shape

Division & Projection

(III) Extraction

(IV) Connection

22

(I)

(V) Rotation

(VI) Vertex connectivity

In (VII,VIII,IX,X,XI,) we divided it into triangles and extracted the center points to the outside of the 3D geometric Shapes.

In (XII,XIII) we decreased the length between each 3D shape. In (XIV) we overlapped some of the elements and that in order to subtract them from each other which it is shown in (XV,XVI,XVII).

(VIII)

(XII)

(VIII)

(XIII)

(IX)

(X)

(XI)

(XIV)

(XV)

(XVI)

(XVII)

In this process we copied form (A) and rotated it, and we subtracted them from each other , and than we added a rectangular extruded grid in order, and we euxcavated form (C) . From this process we found new form.

Form ( A)

Form (B)

Form ( C)

New forms

new moments

celcon plastic model

3D print top view

3D print bottom view

3D print side view

Colored 3D print

Plastic Colored 3D print