Fractal Inceptions

Sirenia Kim, Hajir Al Khusaibi, Ye Xiong

An architecture project is evaluated by many factors; the foremost being whether the form and program are contextual. However, as a group, architects tend to downplay greater community repercussions; namely, gentrification and environmental resiliency. As described in Michael Batty & Paul Longley’s “Fractal Cities: A Geometry of Form and Function,” visual order builds our understanding of cities. Despite variations in conception, urban planning maintains its objective to provide a simple and digestible order to the complexity of our disordered lives.

In our project, we investigate how traditional fractal city planning adjusts to the climate justice movement, and how that then affects financial equity and resident migration.

The 3 main reasons we selected Los Angeles as our case study city are:

from left to right

1. The planning of LA lies somewhere in between organic and planned. (Because of its wide sprawl, certain areas of the city were developed rapidly with individual changes.)
2. The idyllic climate fostered many different nuclei along the Los Angeles river.
3. Since it is a relatively young city, Los Angeles has been a test bed for car-dependent urban travel (which contributes significantly to its environmental concerns).

Built:LA is an interactive map categorizing LA’s buildings by their year of construction. (Designer: Omar Ureta)

Visualization Study #1 of Los Angeles: Population Concentration

using UnityEngine;
using System.Collections;

[ExecuteInEditMode]
[RequireComponent (typeof (Camera))]
public class KaleidoscopeIndieEffect : MonoBehaviour {
public enum EffectType{
Circle,
Triangle60Tiling,
Triangle90Tiling
}
public EffectType effectType;
public int number =6;
public Vector2 center = new Vector2(0.5f,0.5f);
public float radius = 0.5f;
public float angle = 0;
public float scale = 1;
static Material m_Material = null;
public Shader shader ;
static Material m_Material2 = null;
public Shader shader2 ;
void OnDisable() {
if( m_Material ) {
DestroyImmediate( m_Material );
}
}
private Texture2D cachedTexture;
void OnPostRender() {
if(m_Material == null){
m_Material = new Material(shader);
m_Material2 = new Material(shader2);
}
Rect r =GetComponent<Camera>().pixelRect;
int width = Mathf.RoundToInt(r.width);
int height = Mathf.RoundToInt(r.height);
if(cachedTexture == null || cachedTexture.width!=width || cachedTexture.height!=height){
cachedTexture = new Texture2D(Mathf.RoundToInt(r.width),Mathf.RoundToInt(r.height));
}
cachedTexture.ReadPixels(r,0,0);
cachedTexture.Apply();
float xCorrect = r.height/(float)r.width;
//Graphics.SetRenderTarget(destination);
GL.PushMatrix();
GL.LoadOrtho();
#if  UNITY_EDITOR
GL.Clear(true,false,Color.black);
m_Material2.SetPass( 0 );
GL.Begin( GL.TRIANGLES );
GL.Color( new Color(0,0,0,1) );
GL.Vertex3( 0, 0, 0 );
GL.Vertex3( 0, 1, 0 );
GL.Vertex3( 1, 0, 0 );
GL.Vertex3( 0, 1, 0 );
GL.Vertex3( 1, 1, 0 );
GL.Vertex3( 1, 0, 0 );
GL.End();
#else
GL.Clear(true,true,Color.black);
#endif
m_Material.mainTexture = cachedTexture;
m_Material.SetPass(0);
GL.Begin(GL.TRIANGLES);
if(effectType == EffectType.Circle){
int n = (number/2)*2;
if(n<4)n=4;
float angle1 = (angle/360-0.5f/(float)n)*Mathf.PI*2;
float angle2 = (angle/360+0.5f/(float)n)*Mathf.PI*2;
Vector2 uv1 = center+new Vector2(Mathf.Sin(angle1)*xCorrect, Mathf.Cos(angle1))*radius/scale;
Vector2 uv2 = center+new Vector2(Mathf.Sin(angle2)*xCorrect, Mathf.Cos(angle2))*radius/scale;
for(int i = 0 ; i < n ; i ++){
angle1 = (angle/360+(i-0.5f)/(float)n)*Mathf.PI*2;
angle2 = (angle/360+(i+0.5f)/(float)n)*Mathf.PI*2;
GL.TexCoord((i%2==0)?uv1:uv2);
GL.Vertex(new Vector3(center.x+Mathf.Sin(angle1)*xCorrect*radius, center.y+Mathf.Cos(angle1)*radius, 0));
GL.TexCoord((i%2==0)?uv2:uv1);
GL.Vertex(new Vector3(center.x+Mathf.Sin(angle2)*xCorrect*radius, center.y+Mathf.Cos(angle2)*radius, 0));
GL.TexCoord(center);
GL.Vertex(center);
}
}else if(effectType == EffectType.Triangle60Tiling){
int n = number;
if(n<1)n=1;
float angle1 = (angle/360-0.5f/6)*Mathf.PI*2;
float angle2 = (angle/360+0.5f/6)*Mathf.PI*2;
Vector3[] uv = new Vector3[]{
center,
center+new Vector2(Mathf.Sin(angle1)*xCorrect, Mathf.Cos(angle1))*radius/scale,
center+new Vector2(Mathf.Sin(angle2)*xCorrect, Mathf.Cos(angle2))*radius/scale
};
for(int i = 1 ; i <= n ; i ++){
for(int j = 0; j < 6 ; j++){
angle1 = (angle/360+(j-0.5f)/(float)6)*Mathf.PI*2;
angle2 = (angle/360+(j+0.5f)/(float)6)*Mathf.PI*2;
Vector3 up1 = new Vector3(center.x+Mathf.Sin(angle1)*xCorrect*radius*i, center.y+Mathf.Cos(angle1)*radius*i, 0);
Vector3 up2 = new Vector3(center.x+Mathf.Sin(angle2)*xCorrect*radius*i, center.y+Mathf.Cos(angle2)*radius*i, 0);
Vector3 down1 = new Vector3(center.x+Mathf.Sin(angle1)*xCorrect*radius*(i-1), center.y+Mathf.Cos(angle1)*radius*(i-1), 0);
Vector3 down2 = new Vector3(center.x+Mathf.Sin(angle2)*xCorrect*radius*(i-1), center.y+Mathf.Cos(angle2)*radius*(i-1), 0);
for(int k = 0 ; k <= i; k++){
if(j%2==0)GL.TexCoord(uv[(i+k)%3]);
else GL.TexCoord(uv[2-(i+k+2)%3]);
GL.Vertex(Vector3.Lerp(up1,up2,k/(float)(i)));
if(j%2==0)GL.TexCoord(uv[(i+k+1)%3]);
else GL.TexCoord(uv[2-(i+k+1+2)%3]);
GL.Vertex(Vector3.Lerp(up1,up2,(k+1)/(float)(i)));
if(j%2==0)GL.TexCoord(uv[(i-1+k)%3]);
else GL.TexCoord(uv[2-(i-1+k+2)%3]);
if(i==1)GL.Vertex(center);
else GL.Vertex(Vector3.Lerp(down1,down2,(k)/(float)(i-1)));
if(k>0){
if(j%2==0)GL.TexCoord(uv[(i+k-1)%3]);
else GL.TexCoord(uv[2-(i+k-1+2)%3]);
GL.Vertex(Vector3.Lerp(down1,down2,k/(float)(i-1)));
if(j%2==0)GL.TexCoord(uv[(i+k-2)%3]);
else GL.TexCoord(uv[2-(i+k-2+2)%3]);
GL.Vertex(Vector3.Lerp(down1,down2,(k-1)/(float)(i-1)));
if(j%2==0)GL.TexCoord(uv[(i+k)%3]);
else GL.TexCoord(uv[2-(i+k+2)%3]);
GL.Vertex(Vector3.Lerp(up1,up2,(k)/(float)(i)));
}
}
}
}
}else if(effectType == EffectType.Triangle90Tiling){
int n = number;
if(n<1)n=1;
float angle1 = (angle/360)*Mathf.PI*2;
float angle2 = (angle/360+0.125f)*Mathf.PI*2;
Vector3[] uv = new Vector3[]{
center+new Vector2(Mathf.Sin(angle2)*xCorrect, Mathf.Cos(angle2))*Mathf.Sqrt (radius*radius*2)/scale,
center+new Vector2(Mathf.Sin(angle1)*xCorrect, Mathf.Cos(angle1))*radius/scale,
center
};
Vector3 right = new Vector3(Mathf.Sin (angle/180*Mathf.PI+Mathf.PI/2),Mathf.Cos (angle/180*Mathf.PI+Mathf.PI/2),0);
Vector3 up = new Vector3(Mathf.Sin (angle/180*Mathf.PI),Mathf.Cos (angle/180*Mathf.PI),0);
for(int i = 1 ; i <= n ; i ++){
for(int j = 0; j < 4 ; j++){
Vector3 x = new Vector3();
Vector3 y = new Vector3();
if(j==0){
x = right;y=up;
}else if(j==1){
x = -up;y=right;
}else if(j==2){
x = -right;y=-up;
}else if(j==3){
x = up;y=-right;
}
x*=radius;
y*=radius;
x.x*=xCorrect;
y.x*=xCorrect;
for(int k = 0 ; k < i; k++){
GL.TexCoord(uv[i%2==0?2:0]);
GL.Vertex((Vector3)center+(-i+k*2)*x + i*y);
GL.TexCoord(uv[1]);
GL.Vertex((Vector3)center+(-i+k*2+1)*x + i*y);
GL.TexCoord(uv[i%2==0?0:2]);
GL.Vertex((Vector3)center+(-i+k*2+1)*x +( i-1)*y);
//
GL.TexCoord(uv[1]);
GL.Vertex((Vector3)center+(-i+k*2+1)*x + i*y);
GL.TexCoord(uv[i%2==0?2:0]);
GL.Vertex((Vector3)center+(-i+k*2+2)*x + i*y);
GL.TexCoord(uv[i%2==0?0:2]);
GL.Vertex((Vector3)center+(-i+k*2+1)*x +( i-1)*y);
if(i>1&&k<i-1){
GL.TexCoord(uv[i%2==0?2:0]);
GL.Vertex((Vector3)center+(-i+k*2+2)*x + i*y);
GL.TexCoord(uv[1]);
GL.Vertex((Vector3)center+(-i+k*2+2)*x + ( i-1)*y);
GL.TexCoord(uv[i%2==0?0:2]);
GL.Vertex((Vector3)center+(-i+k*2+1)*x + ( i-1)*y);
//
GL.TexCoord(uv[i%2==0?2:0]);
GL.Vertex((Vector3)center+(-i+k*2+2)*x + i*y);
GL.TexCoord(uv[i%2==0?0:2]);
GL.Vertex((Vector3)center+(-i+k*2+3)*x + ( i-1)*y);
GL.TexCoord(uv[1]);
GL.Vertex((Vector3)center+(-i+k*2+2)*x + ( i-1)*y);
}
}
}
}
}
GL.End();
GL.PopMatrix();
//GL.Clear(true,false,Color.black);
}
}

Visualization Study #2

Visualization Study #2 with Attractor as Variable