ACD_SM1/2021_Assignment 1_Guangen Jin

Randomness as a Generative Principle - Point

Construct origin point

1 Input of points

2

8

Restrain in an isosceles right triangle area from the point

New points as input and loop 1-8 for the next round

Week 1 Randomness Strategy

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7 Take out all the new points

Randomly generate points within the area

Loop twice

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4

Repeat 2-5 on the opposite side

Select two points within the area

5 Lines between output and input points

Step 1 -5

Step 6-8

First loop

Second loop

Randomness as a Generative Principle - Line

Apply thickness on tree branch

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4

Geometry of a tree branch

Scale horizontally to vary the shape

Combine and merge branches together

Duplicate and shift horizontally

From line to surface

Step 1

Step 2

Array of the tree surface and divide

Step 4 loop

Additional thickness given to the connection edge to bend surface 90 degrees.

Additional thickness given to the connection edge to bend surface 90 degrees.

Step 3

Generate tree pattern in the same method as the analysis of the precedent.

Alternate Sub-division from Octahedron A geodetic dome can be generated with an octahedron by projecting triangles toward the spherical surface. A similar workflow is considered in the dome surface pattern.

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Move tree branch on the triangle surface of octahedron

Extended Lines intersect with hemisphere

Reconnect points on the hemisphere

Rotate and duplicate as a group

1 Equally divide the tree pattern

Circle to hexadecagon To make the cost of the facade lower, the cylinder is turned into a regular hexadecagon. Tree pattern from the precedent is divided into 8 parts equally.

2 Trim and frame the pattern

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3 Repeat panel from 1-8

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Y shape in the square

Rotate 90 degree

Rotate 180 degree

Repetition and rotation of line Randomness is created by repeating and rotating a group of intersecting lines. After that, trim the lines with a rectangle region.

4 Array and rotate the shape in step 3

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Trim with the rectangle

Isometric view of warpped facade

6 Divide into four equal parts

Repetition and rotation of line The logic is the same as the last one, but the line pattern is stacked in the vertical direction.

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Pattern from step 5 in the last exercise

Mirror horizontally

Array in horizontal directly

Wrap to the facade

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Ar

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Dr

Repeat the surface pattern Eight different panels share the same pattern at their perimeter, allowing the panels to be tiled seamlessly to generate an embroidered effect across the entire envelope.

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Week 2 Randomness with Grasshopper Randomness by Gaussian function The pattern of the surface is controlled by three inputs (a,b,c) of the Gaussian function. The angle and distance between the gravity centre define the rotation and scale of the ‘Y’ shape pattern.

b a

c

Three inputs to control the shape of Gaussian function. The gravity centre of the concave/convex area is marked.

The farther distance between ‘Y’ and Gaussian function centre is, the smaller ‘Y’ shape is scaled.

The centre line of ‘Y’ is oriented toward the gravity centre of the concave/convex area of the function.

Step 1: Vertices of 4 x 4 lattices are generated.

Step 2: Duplicate ‘Y’ geometry on the lattice by matching the ‘Y’ geometry gravity centre and vertices

Step 3: Gaussian curve define the scale and rotation of the ‘Y’ Geometry.

Step 4: Trim the geometry with 4 x 4 rectangle.

Step 5: Apply the thickness to the curves.

Variation by changing the Gaussian curve

Week 3 Randomness wtih Recursion Recursion and Loop The following diagram explains the running of the recursion function until the counter of the loop structure reaches 5 times.

Step 1

Step 2

Step 3

Step 4

Vector 2 Vector 1 Vector 2 Vector 1

1. Create an empty curve list (list a) and a Gaussian curve.

2. Append the line-like curve into the empty list (list a).

1. Define the recursion function with variables (gh_ curve, angle, and counter). Create an empty list b.

2. Define a new_curve by copy and move the gh_curve, scale to 80% of the original length.

1. Create new_vector direction by plus vector 1 and 2.

2. Rotate new_curve by the new created vector.

1. Copy and rotate the new_curve to the left and right separately by 30 degree.

2. Append left and right curve into list b.

Loop 1-5, when counter = 5, end the loop.

Loop 2 1. Call the recursive function from step 2-4.

2. Input variables: list a, angle = 30, counter = 5

Loop 3

Loop 4

Loop 5

Different Iteration The Gaussian curve is used to generate different recursive patterns, which is stepped on the previous stage.

b = -2

b=0

Iteration 1

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Iteration 2

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b=2

Iteration 3