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Man Keung Lee 551518


About Me

Hi, my name is Man Keung Lee. I am majoring in architecture in the Bachelor of Environments at The University of Melbourne. I come form Hong Kong and this is my third year in Melbourne. The building environment between Melbourne and Hong Kong is quite different as Hong Kong is well known for its skyscrapers. Melbourne gave me totally different feelings with is flat land and suburban house. And I do enjoy my life in Melbourne, especially its fresh air which Hong Kong lacks. As an architecture student, I loves classical buildings more than the contemporary buildings because of their regularity, order and sublimity. So air studio is a very good chances for me to take a deep look in the contemporary building using parametric technology. And I believe it is the future of architecture as the use of parametric technology makes complex geometry in building

possible and it could utilize the material more effectively and efficiently.

Software experience Before doing Virtual Environment, I have never used computer for designing. In that studio, I started to explore Rhino as a tool of designing and I also used panelling tool plug-in to help creating the digital model. I also started using InDesign and illustrator to construct my journal. I could do basic function with them, by honestly I am not an expert in them so I still have a long way to master them well. In water studio and Construction Design, I started to use AutoCad to draw plans, elevations and sections. After water Studio, I realize that I lack the ability to present the digital model nicely, so I started learning Cinema 4D as a rendering tool.

Virtual Environment Design

Water Studio Design



Part A - Introduction A.1. Architecture As Discourse


A.2. Computational Architecture 11 A.3. Parametric Modelling 15 A.4. Conclusion 19 A.5. Learning Outcomes 20 A.6. Appendix - Algorithmic Explorations


Part B - Design Approach B.1. Design Focus 28 B.2. Case Study 1.0 30 B.3. Case Study 2.0 34 B.4. Technique: Development 40 B.5. Technique: Prototypes 50 B.6. Technique Proposal 56 B.7. Learning Objectives and Outcomes


B.8. Appendix - Algorithmic Sketches



Introduction - Western Gateway Design

In order to upgrade the condition and aesthetics of Wyndham City’s environment, the city council established this Gateway Project. It was aimed to inspire and enrich Wyndham City. The design needs to be ‘longevity in its appeal, encourage ongoing interest in the Western Interchange by encouraging further reflection about the installation beyong a first glance’[1]. The project would be located within a very flat and wide open landscape. It also needs to make an impact for high speed movements. It should be accessible to a wide public and should explore place-making aspects and qualities[2].

[1] [2]

Key consdierations: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Prominent location of the site at the entry to metropolitan Melbourne. Back dropped by a large scale service centre Consideration of how the installation integrates with and/or sits in the immediate and surrounding landscape Iconic feature Appropriately scaled Dialogue between sculpture and landscape to compose the Gateway Original and engaging in form Object-centred individual sculpture or a more experimential approach Literal or abstract Adherence to the regulations imposed by VicRoads in relation to siting, view lines, setbacks, material, colours etc Daytime and night time viewing Safety, ease of maintenance, material and longevity

Architecture as a Discourse

‘Ideas are not innate but provisional.’ [3] Architecture is meaningless without users. It is a medium to transfer ideas. Its quality and beauty is defined by users. Everyone might perceive different feelings. And it changes under the change of time, weather and mood.Feelings change when the context changes. So does architecture. With the aid of digitalization, we are now able to make significant improvement in the design of architecture. Pure form, complex geometry, material propesties could be well considered in the design process.

[3] Hill, Jonathan (2006)


Precedent one - Church of Light

Tadao Ando used to emphasize nothingness and empty space to represent the beauty of simplicity. It is a church with contrast. Reinforced concrete is the major component of the church, which normally gives a sense of heaviness,lifeless, and etc. However, all this characteristics were perfectly utilized to make contrast to the light. The cross in the front changes the mood totally. The lights penetrated define the volumne of the interior space. The church is not for sight seeing, but praying and worshiping. In the renaissance/ baroque cathedrals, lights are penetrated from the top, which symbolized Heaven and God. Ando made a different approach, where lights are penetrated from forward. Yet, it gave a feeling of divinity and also a sense of

welcome from God. Ando made a step forward from the old ages.


Salk Institue for Biological Studies - Louis Kahn

‘Architecture must be immaterial and porous, as well as solid and stable where necessary.’ Hill, Jonathan (2006) Salk Institute demonstates how a good architecutre should be accoding to Hill and Jonathan. It is the modernist attempt to frame the atmosphere with architecture. It consists of two mirror-image structures that flank a grand courtyard.The use of repetition and strong axiality, emphasized the simple geometry of the surrounding buildings. These building blends with the nature in harmony as shown in the images. It is still using as its original function, but there are also architectural tours for those interested to know more about this award-winning architecture. It has also been described as the single most significant architectural site in San Diego.


A.2. Computational Architecture ‘Scripting is a voyage of discovery. ‘ Burry, Mark (2011) In this information age, our lives are closely bound with computer. In architectural field, the word computerization and computation have always been misunderstood. While the former one is the use of computer to design, such as using AutoCAD to digitize the documentation, the latter one is the use of algorithm in the process of design. Not only allow architects to design buildings with complex geometry, it expands the possibility of design with the consideration of material properties. ‘With the aid of computational design tool, material behaviroal characteristics are integrated as parametric dependencies based on a large number of physical and computational tests. Thus, architectural form, material formation and


structural performance can be considered synchronously.’ Fleischmann, M., Knippers, J., Lienhard, J., Menges, A. and Schleicher, S. (2012) ICD/ITKE Research Pavilion is a perfect example of computation design considering material behavior: The shape of the final outcome is determine by the elastic bending of plywood, which forms the elastically bent arch structures. The research pavilion’s structure is entirely based on the bending deformation of thin birch plywood strips within the elastic range. This is different from most of the architectural design, where normally the architect will design the shape of the final outcome. Material itself does not play an important role to the design of shape. However, this project demonstrates another path of design where material properties were fully investigated and driven the shape of the product.

Another main difference of computation design compared to the ordinary design process is the close relation between architect and manufacturer. ‘The manufacturing and assembly logics were integrated in the computational process.’ Fleischmann, M., Knippers, J., Lienhard, J., Menges, A. and Schleicher, S. (2012)


a huge improvement on the precison between the product and the design, as architect can control every small detail of the construction process. More creative potential of the design could then be exploited ‘Architects have started to integrate fabrication as a generative paradigm into the design process.’ Gramazio, F., Kohler, M. and Oesterle, S. (2010) Therefore, fabrication-relevant decision would be included in the early design process. With the material properties data provided by the manufacturer, architect would be able to control complex interactions between singular material elemnets, and produce the machining data directly. It can foresee that the tightening bond would make


West fest pavilion project is an good example showing the precision of computeraided manufacturing (CAM).

‘So when we use methods of computation, it is not a technology that we try to do something with it; the focus is more on design intent and the architectural idea and concept. We try to find the right tool, and develop the tool to make the concept work.’ Peters, Brady. (2013) ‘While he admits that there is often an ornamental aspect, the designs are not primarily visually driven. The generation of geometry and material configurations are performance driven.’ Peters, Brady. (2013) It might be a trap for architects that more and more complex geometry can be achieved through computation. However, it is a tool to aid architects to design, not a tool constraining the design of architects. Design ideas should always be the centre of the architecture, not its geometry.


Nordpark Carble Railway Zaha Hadid Architects

A.3. Parametric Modelling

Using the new production methods such as CNC milling, the manufacturer can ensure the precision of the building with the digital design. It successfully achieved a streamlined aesthetic which could hardly be done without the aid of computation. Undeniably the building is impressive with its fluidity. It is arguably that whether the design blends into its context nicely, as its soft form is quite different from the rigid buildings in the surroundings. However, like many of the other computation design, this building is much energy efficient than most of the building using contemporary design method. The use of computation can modify every smallest detail of the architecture to provide the best energy outcome. Also, its great flexibility also makes it adaptive to the change in the topography.

Parametric design is still a developing style in architecture and there is a long way to gain the society, business and political acceptance. As discussed in the previous section, computation is a process of discovery, where architects might not be able to give the exact outlook at the very first start of design process. Investor might be impatient as architects need to vary the parameters to find the best possible outcome. In the reality, the greatest concern of the clients are the interest of investment, the increasing time of design might lead to increasing amount of cost.

time is required. ‘A far greater range of potential outcomes for the same investment in time.’ Burry, Mark (2011) Using computation, different potential outcomes can be generated easily through changing of parameter, therefore it gave more choice for the clients to choose the best outcome.

Although the design period might be longer, the fabrication would be much easier as manufacturers can start fabricating using the data provided from the architects. Therefore, less construction


Cardboard Cathedral

Cardboard Cathedral is built in attempt to temporarily replace the old 19th century Anglican cathedral that was damaged by the magnitude-6.3 earthquake in 2011. As there is a need to build a new cathedral for the community, this temporarily Cathedral is built so that people can have a place to pray, worship and hold events and concerts. It is a waste-sensitvie house that is made of paper tube, a recyclable, low-cost and remarkably resilient material. The frame structure is built from timber, stell, 98 polyurethane and flame retardantcoated cardboard tube. Though the material seems cheap and not particular strong, Cardboard Cathedral is built to last with a lifespan of five decades. And it is 100 percent up to earthquake code. Though it is not appealing,

the Cardboard Cathedral did achieve many of its brief. As in an inspiration to our project, the use of composite material in this building reduces the material cost, yet still providing a satisfying lifespan and performance. Cheap, soft material can be turned useful if its properties were being used effectively and combined with the other material. This will be what we are trying to achieve, combine materials with different properties to provide a final structure with good performance and attracting outlook. Computation is needed as they help investigating propeties of materials by converting them into digital parameters.


A.4. Conclusion

As mentioned above, my philosophical idea of architecture is that it is a journey, an experience to continuous discovering. And this will be the main idea of the gateway design. Users will be refreshing and fascinating by its abstract appearance. Parametric design will be used since it helps integrated the design and fabrication unit. It is presumably that there will be limited construction hour to avoid disturbing the traffic. Parametric design integrated the fabrication unit in the early phase of the design process, and a more precise result would be achieved due to the use of CNC manufacturing. Given the greater ability to control details, individual parts of the design will be adjusted to fit in the context to make it blend with the environment. Also, it will be a design that interacts with the atmosphere which aimed to produce a design that frame the

nature. Composite materials will be used in the design, where properties of different materials will be converted into parameters in the designing tool in order to produce a efficient outcome. These materials will be combined together in order to produce a design that balances the efficient and the lifespan.

A.5. Learning Outcomes

As doing this assingment, I became more familar with parametric design and computation method. At first I though computation is the same as computerization, which I found this was a common misunderstaning towards parametric design. I became more familiar about the change in design and construction process under computation. Although I have not gone very deep in the practice of parametric design, I saw its ability to generate fascinating geometry in a short amount of time, which could never be done easily using comtemporary method. Moreover, it enables changes of the detail by changing the parmaters. It is all about doing experiments with the deisgn and to discover properties of the design.


Week 1 Grasshopper Tutorial




A.6. Appendix - Algorithm Exploration





Week 2 Grasshopper Tutorial





2.2 Vector defining direction, magnitude, scaling, ratio and rotation: Vector can be added directly using addition. 2.3 Mesh Geometry Loft (infinite curve) vs mesh (shortest distance) Use of quad corner, point list, point, construct mesh. 2.4 Brep - boundary representation.


Week 3 Grasshopper Tutorial



3.1 Parametric concept Align, draw icon, edit>group } help organizing the data.

3.2 Point, list and data matching Three rules to sort the list: 1. shortest list 2. longest list - last three are use for same origin 3. Cross reference - all possible choice


Part B. EOI II: Design Approach

B.1. Design Focus

Group Argument Our group decided to focus on geodesics as the field of interest. A geodesic is the shortest route between two points on a surface. With the aid of parametric tools, it is possible to apply geodesics to complex geometries that could hardly be done in the past. The scope of geodesics construction has a lot of possibilities and it is very efficient. It can minimize the material use yet maximize the architectural presence in space. With this parametric approach, it could help create a massive structure with less material, and we believed that we could bring an astonishing impression for the drivers passing through the gateway.


Montreal Bioshpere Buckminster Fuller

B.2. Case Study 1.0 Doing more with less The Montreal Biosphere was built by Buckminster Fuller for the 1967 World’s exhibition. The biosphere was donated to the city of Montreal later by the US goverment. The biosphere was built out of steel pipes and large pieces of acrylic paneling. The biosphere demonstrated several Fuller’s attempt to improve human shelter: applying modern technological to shelter construction; making the shelter more comfortable and efficient; making shelter more economically availiable. [1] The sphere was attempted to enclosed the largest volume of interior space with the least amount of surface area thus saving on material and cost. The sphere uses tiangle as panel because it helps to resolve the force inside the supporting members. This kind of system utilize gravity rather than opposing

it, whcih can create a strong nad light construction similar to airplane [2]. We are particular interested in this building because of its efficient use of material and the ability to create maximum interior space. In the gateway project, the design should be accessible to a wide public, therefore we would like to create an architecture with great interior space, so that more people could be able to enter it if there is any event hold inside the structure. Also, the efficient use of material allows us to build a massive structure with less material, since the gateway project should be eye-catching in the first glance, we would like to build a gigantic sculpture in the site.

[1] [2]


1. Quads Panel

2. Random Quads Panel

3. Staggered Quad Panel

4. Triangle Panel B

5. Triangle Panel C

6. Triangle Panel A

7. Brace Grid 2D Structure

8. Grid Structure

9. Diamond Grid Structure

10. Hexagonal Structure

Parametric Diagrams As there is no definition provided in LMS for grids and lattice, we then looked at the lunch box plug-in in grasshopper. It could be used to generate panels for a surface very easily. First, we created a basic geometry, which would be applied panels later on. In lunch box, we could choose either applying panels or create a structure over the surface. We found that the use of applying panel could be found in many of the contemporary architecture, as it could help to construct a complex a geometry into a more fluid shape if there is more nodes inside the structure.

1. Creating geometry

We can also create our own panels and structure grid using lunch box, which give a different feeling compare to basic quad, triangular structure. The highlighted result are more successful since they are able to rebuild the sphere closely better. If we want to create a more fluid design using lunch box, quad, and triangular panel are prefer rather than diamond and hexagonal structure, as the increasing number of sizes make it hard to cover the whole surface smoothly. Also, increasing number of UV helps to create a smoother surface, howerver, it may also increase the calculating time. However, there is a limit in the use of lunch box. Although user could create their own panel, the basic geometry constraints the shape of the final structure. Therefore we need to find another way for form finding in our design.

3. Creating Structure

2. Creating Panel


Canton Tower

B.3. Case Study 2.0

The Canton Tower is the world’s tallest TV tower [3] designed by Information Based Architecture. The tower is very slender and tall, as the designers wanted to design a free-form tower like a female figure, being complex, transparent, curvy , gracious and sexy [4].

I would like to design to demonstrate curvature and fluidity because these properties gave an energetic impression. This case study could be used to show how a building could be made curvy and sexy with steel columns.

The form, volume and structure is generated by two ellipses, one at foundation level and the other at a horizontal plane at 450 metres. The structure consist of a open lattice-structure with 1100 nodes [5]. Since skyscapers are usually assoicated with the feeling of lifeless, the Canton tower made a good attempt to embed human properties in the building. As the gateway project will be located next to the highway, the drivers driving through would quickly get bored by the design if it is lifeless and oridinary.

[3] [4] [5]


First Attempt to rebuild Canton Tower

In the first attempt rebuilding the Canton Tower, I used a rather sample method. The first thing is to determine the geometry of the tower. Then, several curves were created and lofted later to obtain the geometry. Using lunch box plug in, the loft surface could be resolved into a grid structure. Using the photos of the Canton Tower as a reference, we found that the digital model would look like the tower better using diamond grid structure. As a result, a diamond grid would be applied to the loft surface, we then apply a pipe component in order to visualize the grid lines. As the actual tower used 1100 nodes to create the whole structure, we increased the number of UV in order to get the closest number of nodes.

At the first glance, the digital model looks alike the Canton Tower, but when we looked at the tower again, we found that the grid structure was a bit different from the digital model. Rather than simplily applying the structure, the actually tower looks like being twisted. Also, the steels enclosuring the surface have differnt radius, so it is not uniform as what I have done in the pipe component.


Second Attempt to rebuild Canton Tower

Other than lofting the curves and applying the panels, I tried to look at differnt ways to rebuild the tower. I do another research in surface blending in grasshopper. 1. Create the basic curves. 2. Divide the surfaces and construct lines between the surface. 3. Evaluate the lines and create points in a desinated position. 4.Create a new surface from the points evaluated . This method is quite diffent form the first method. Because the new surface created shows the transition of the surfaces while there is no relation between surface in the first method. We found that the this kind of method have a greater possiblities in the form making process. Using reverse, a differnt shape of transition surface would be obtained and using the populate 2D command, we were able to put the lines in different positions

rather than a evenlly divided distance.

B.3. Case Study 2.0


Development Process

Grasshopper action

Case Study

Lunchbox Plugin

Exoskeleton Plugin

Further Research

Minimmal Surface

Surface Blending

B.4. Technique: Development



Wireframe Thickening Proposed Design Form Finding

Form Finding


Further Research: Exoskeleton Base Geometry

Exoskeleton is a plug-in a grasshopper that turns network of lines into solid. The thickness of the structs, node sizes and whether to leave openings only one connected line could be altered in the settings.

B.4. Technique: Development


Further Research: Minimal Surface Base Geometry

In order to search for grasshopper operations to determine the form of the design, we tried to do some research in minimal surface using kangaroo plug-in. Starting from a cube, we tried to apply the script to see what will happen, and by altering the rest length, it will alter the final outcome We then tried to examine it with a more complex geometry:

exploding the cube and removed some of its face; boolean the object with another solid. The results were quite satisfying and some interesting geometry would be generated. We found out that it is very easy to create an interesting form using kangaroo, however, it left little space for us to further develop the form. Also, the base geometry has a huge influenced to the final outcome so if we want a different

B.4. Technique: Development

outcome, we would need to start from the base geometry.


B.4. Technique: Development

Matrix Using two surface as a base and top plane, I tried to explore the possibility by altering different values. The shapes of surfaces, the number of division, order of the lines, number of transition plane, position of the transition plane, the thickness of the pipes, the panels covering the surface and the structure that formed the surface were altered to find the best aesthetic outcome.


Vector Diagram

1. 2.

The logic of the model in grasshoppers consists of four major steps: 1. In order to show the transition in surface, there are two surfaces created . One is the base plane and the other is the surface that being transformed. At the moment, we only used a loft surface created by our own so there is a lack of connection between the transformation. We tried several

commands in kangaroo to simulate the physical performance when a plane is being pulled but we could not get a satisfying result so we used a free form loft surface instead. 2. The second operation is to divide the surfaces and create lines between the surface.

B.4. Technique: Development

4. 3.

3. It is the most critical process of the model. The lines were evaluated and a new surface would be formed to according to the position of the lines. This surface aims to show the transition between the base plane and the top surface.

4. Triangular pannel would be applied to the surfaces and the lines would be piped in order to make them thicker.


Composite Material

We have chosen to investigate composite material as we believed it has the most flexibility in architecture. In our definition, composite material refers to the combination in use in two or more materials. They need not to undergone chemical reaction to create a new material with different properties. Yet, those two

materials should be worked as a close system that each of the material is inter-dependent to each other. Therefore, if one of the material is missing, the whole system collapses.

B.5. Technique: Prototypes

We chose wire, rope, cardboard paper and plain paper as the starting point of our material experiment. In order to let these materials work in system, we thought of ways to connect the materials into one. We thereby punched holes on the surface and let the rope and wire embedding into it. Positioning the holes in different pattern and crossing the

ropes in different patterns, we found out that the surface would deform differently as we pulled and twisted the surface and ropes in different direction. We are particularly interested in the transformation of the surface when we pulled the ropes in different magnitude of forces. Also we were interested in the geodesics the ropes demonstrated. 50










7 In order to fabricate our model, we have exploded the surface and rejoined them as different strips. It could be then unrolled into a flat surface. We marked the score and the cut line into different colors (e.g. score = red; cut = black) according to the guide of Fab Lab and we cut it out manually using the paper cutter.


During the digital modelling, we did not consider the joints between the material very well. At first, we only created holes that fits the plastic tube in the strips and we cut the marks in the tubes so that the paper can embed into the tube.

B.5. Technique: Prototypes

However, the connections did not work well so we think of another ways to connect the layers and the tube. We make a circle clips with a hole that are slightly smaller than the tubes. Glues were applied to connect the layers and the clips. Before constructing the model, we thought the little walls we made would be enough to make the model stand as the whole system is intentionally decided to be self supported: the membranes would hold the tubes in place. Nevertheless, as the tubes are positioned in different angles, they are hard to keep in a certain angle without falling, so we sticked the pin to hold the tubes in place.


B.5. Technique: Prototypes


Proposed Design

Concept Wyndham city is undergoing a rapid development, population is estimated to be triple in the near future. Therefore, the proposed design aims to manifest a feeling of transformation. The design also tries to correspond to the previous project ‘Seeds of Change’, emphasizing we are following the path of change ten years time later. Interactivity The design adopted an open design and is located outside the service station, so that visitors could access the gateway and spend their time there.

Inspiration Originated from the bottom layer, the top three layers show the transitions from bottom to top. None of the layer is either superior or inferior and they are equally important. The design is attempted to encourage visitor to rethink what they have gained and lost during the transformation: the lost of green space? The gain of prosperity? Longevity The irregularity in shape makes the design have longevity in its appeal. Therefore drivers would have different views everytime they pass through the design.

B.6. Technique Proposal


Given the feedbacks from the midsemester presentation, our group did realize a lot of weaknesses in our project. First and the most important, the lack of connection between the material chosen and the design. We defined composite material as a system, which all materials are closely related, however, our design fail to achieve such goals. We found it hard to link our concept of transformation, geodesics and composite material together. Second, the design is not site responsive. We put too many focus on the concept but the model could not demonstrate the concept so it is rather disappointing. The design should be able to interact with the surrounding environment. In the next phrase, we need to consider the design with the landscape. Also, we would try to include others paramaters in the site that would affect the form.

Third, I found there was a lack of focus in the use of grasshopper. Our group have researched some other grasshoppers operation in order to enrich the design. Nonetheless, we did not investigate in depth in any of the operations, which makes our design is simple in the algorithm, yet chaotic in its appearance. Certainly there is a lot more we need to work on to implement our design in order to get a more satisfying result. In the following, our group should focus on the materaility. The design should be able to demonstrate a composite system that materials are closely bound. We will do an in depth research in tensegrity physcially and digitally. As the preliminary model was commented too dense and not elegant enough, we will try to make a better model in the final presentation.

B.7. Learning Objectives and Outcomes

Although we did not produce a satisfying model, I did learn a lot during the design process. In this phrase, we are getting familiar in the use of grasshopper, and the reverse engineering in the precedent projects help us to explore a broad range of commands in grasshoppers, we were able to create our own algorithm. The use of parametric tools also help us to produce many inspiring and unexpected outcome.


1. Create rectangular grid 2. Construct a point 3. Distance between attractor points and grids point as radius of circle 4. Divide the distance if it is too big for the radius 5. Extrude.

Week 4 - Attractor Point

1. Create rectangular grid 2. Image samplier, use filter to set to brightness 3. Use the points to create circle

Week 5 - Image sampler

B.8. Appendix - Algorithmic Sketches

The triangulation could be done using relative item or lunch box plug in. It is useful as the triangle on the surface could be form a strip and unrolled into flat surface. It helps to fabricate model with complex or curve geometry.

Week 6 - Triangulation

The fractal pattern is done using cluster component. This operation is quite interesting as it can be used to constrcut complex geometry by using a series of cluster component.

Week 7 - Fractal


Week 4 Grasshopper Tutorial




B.8. Appendix - Algorithmic Sketches





Week 4 Grasshopper Tutorial

4.1 Creating List Domain: space defined by two numeric extremes(min-max) floor and ceiling. 4.2 Spiraling The use of point polar to define a point. 4.3 Phyllotaxis and Expressions Boolean Toggle: only true or false. Use of panel: multiple text 4.4 Exploring surface geometry Params - container, help to things How to find a point on the surface? Using evaluate surface.Display>preview plan radius. MD slider - can move XY at the same time, set xy domain. Or Add Params> geometry>surface> right click (reset param) 4.5 Field Fundamental Use of point charge, line charge and merge field. Direction display - color Tensor display - arrow 4.6 Expression

B.8. Appendix - Algorithmic Sketches


Week 5 Grasshopper Tutorial




B.8. Appendix - Algorithmic Sketches


5.1 Defining Data Tree condition Don’t flatten (because it removes all levels of data treee resulting in a single list) and don’t do path mapper. 5.2 Navigating Data Structures 5.3 Tree statistic and visualization Tree statistic tells how many things in each branch. Everything is common can get rid of using simplifying tree 5.4 Tree Demension


551518 mankeunglee partb eoi