## Regenerative Urban Arcology

An attempt to * reconnect* people in the city with

**and the process of**

*nature***while adopting alternative**

*growing our own food***through a**

*sustainable construction methods***.**

*modular mycelium approach*
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# Tag: Nature

## Growing Homes

## Regenerative Urban Arcology

## The man-made cocoon

## Spirulina Bank

## The Palm Arms

## Mimicking the Geometry

## Palm Wine

## Alternative Fuel

## Future Proposal

## Nepenthes

## Plants, Math, Spirals, & the Value of the Golden Ratio

# 1.0 Phyllotaxis Spirals

### 1.1 Rational Numbers

### 1.2 Irrational Numbers

### 1.3 Quantifiable irrationality

### 1.4 Phi

### 1.5 The Metallic Means & Other Constants

### 1.6 Why Spirals?

## Thin Film Interference

## Objectivism, Ecology, Ecosystems, Cybernetics, Feedback loops, Californian Ideology, Systems Theory…etc…

## The Nature of Code on Grasshopper

## The Nature of Code

An attempt to * reconnect* people in the city with

A man-made cocoon woven from biodegradable rope material inspired by

the weaving of silkworms. It can be constructed in any softwood tree that

is strong enough and that has a convenient distribution of branches. The

tree is scanned and converted into a 3D model where a custom cocoon design

is created. The cocoon is both lightweight and strong as it is a tensile

structure (secondary structure) wrapping around a tree (primary structure).

It aims to bring people from the city closer to nature.

Trees & Humans

The following images will introduce my artefact into wider context. There are two possible scenarios, which could benefit from my artefact, one of which will be further developed in the upcoming term:

1) forest bathing as a way to for the human to reconnect with nature

2) rewilding as a way to both regenerate the land and human spirit

**Photogrammetry**

OBJECTIVE

The aim of photogrammetry was to create the most realistic three-dimensional representation of a tree, which could then be incorporated into computational experiments making the design process much more efficient.

LIMITATIONS

Photogrammetry generated about 60-70% of tree volume leaving out the detailed branches at the outer ends of the tree. 3D scanning would be a possible solution, however, unavailable at the moment.

**Combining the Virtual and Real**

REAL

3D-model of a real tree

VIRTUAL

wrapping/weaving around the 3D-model of a real tree virtually

**Connecting points in space**

OBJECTIVE

This section of my portfolio focuses on exploring the ways in which points can be connected with strings – in both two and three dimensions. The gained knowledge from this section informed my virtual weaving experiments (previous section)

LIMITATIONS:

When connecting regular geometries, it is much easier to find the differences between different connection techniques. The result looks also much more organised and neat. However, what I am aiming to do is apply these connection techniques to irregular geometries of trees, which is a big challenge.

Wrapping & weaving around real trees

This part tracks my learning of the weaving behaviour of silkworms. I have done my own weaving experiments, both physical and virtual to try and understand how weaved tensile structures work. Going forward, I would like to incorporate some of the observed physical principles into my design (into the Grasshopper script).

Palm trees are angiosperms, which means flowering plants. They are monocots which means their seeds produce a single, leaf-like cotyledon when they sprout. This makes palms closely related to grasses and bamboo.

This mature palm shows how the pattern originally seen in the young plant, forms a distinct mathematic pattern known as ‘Phyllotaxis’. This is a pattern with reoccurs throughout nature and is based on the Fibonacci sequence. In order to try to understand the use and formation of the palm fibre, the overall formation of the palm stem needed to be mathematically explored.

However, redrawing the cross-section of the base of the palm plants allows a better understanding of the arrangement of the palm plant.

This exercise allows models to be made to recreate the patterns found in palm plants. By engineering plywood components, the basic shape of the palm geometry can be made into a physical model.

This was pushed further by curving the plywood components to make extruded palm structure models

The arrayed components can then be altered so that the base of the models form regular polygon shapes. Doing this allows the potential for the structures to be tesselated. Using different numbers of components mean the structure can then be tested for strength.

There are hundreds of used for palm fruits, this the plant producing materials which range from durable, to flexible to edible. One of the more interesting ones if the production of palm wine using the sap from the tree. Within 2 hours of the wine tapping process, the wine may reach up to 4%, by the following day the palm wine will become over fermented. Some prefer to drink the beverage at this point due to the higher alcohol content. The wine immediately begins fermenting, both from natural yeast in the air and from the remnants of wine left in the containers to add flavour. Ogogoro described a ‘local gin’, is a much stronger spirit made from Raffia palm tree sap. After extraction, the sap is boiled to form steam, which is then condensed and collected for consumption. Ogogoro is not synthetic ethanol but it is tapped from a natural source and then distilled.

To understand the fermentation process more clear, the process of fermenting sugar to make wine has been undertaken.

The distillation of the wine can be used to make bio-ethanol. This production of this fuel can act as a sustainable alternative to fossil fuel energy, which is overused and damaging to our environment.

The developed structure, as well as the production of palm wine and bio-ethanol, can be collaborated to develop a programme, which provides sustainable energy, within a space that is inviting and exciting.

The production of bio-fuel releases a lot of carbon dioxide. In order to ensure the process does not impact the environment, this needs to occur inside a closed system, so the CO2 does not enter the atmosphere. This can be done by using the properties of a Solar Updraft Tower. Carbon dioxide released from the fermentation and distillation processes can be received by palm trees for increased photosynthesis, while the excess oxygen from the trees provides fresh air for visitors.

The fermentation process can be controlled within an isolated area of the model.

The Distillation process, which requires a store of water for cooling, can also be conducted in an isolated area of the model, with apparatus incorporated into the structure.

The final proposal will be a combination of all three forms

The natural world is brimming with ratios, and spirals, that have been captivating mathematicians for centuries.

The term *phyllotaxis* (from the Greek *phullon* ‘**leaf**,’ and *taxis* ‘**arrangement**) was coined around the 17th century by a naturalist called Charles Bonnet. Many notable botanists have explored the subject, such as Leonardo da Vinci, Johannes Kepler, and the Schimper brothers. In essence, it is **the study of plant geometry** – the various strategies plants use to grow, and spread, their fruit, leaves, petals, seeds, etc.

Let’s say that you’re a flower. As a flower, you want to give each of your seeds the greatest chance of success. This typically means **giving them each as much room as possible to grow, and propagate**.

Starting from a given center point, **you have 360 degrees to choose from**. The first seed can go anywhere and becomes your reference point for ‘**0**‘ degrees. To give your seeds plenty of room, the next one is placed on the opposite side, all the way at **180°**. However the third seed comes back around another **180°**, and is now touching the first, which is a total disaster (for the sake of the argument, plants lack sentience in this instance: they can’t make case-by-case decisions and must stick to one angle (the technical term is a ‘*divergence angle*‘)).

Next time you only go to **90°** with your second seed, since you noticed free space on either side. This is great because you can place your third seed at **180°**, and still have room for another seed at **270°**. Bad news bears though, as you realise that all your subsequent seeds land in the same four locations. In fact, you quickly realise that any **number that divides 360° evenly yields exactly that many ‘spokes.’**

Note: This is technically true with numbers as high as 120, 180, or even 360(a spoke every 1°.) However the space between seeds in a spoke gradually becomes greater than the space between spokes themselves, leaving you with one big spiral instead.

These ‘spokes’ are the result of the periodic nature of a circle. When defining an angle for this experiment, the more ‘*ratio*nal’ it is, the poorer the spread will be (**a number is rational if it can be expressed as the ratio of two integers**). Naturally this implies that a number can be irrational.

Sal Khan has a great series of short videos going over the difference between the two [Link]. For our purposes, the important take-aways are:

-Between any two rational numbers, there is at least on irrational number.

–**Irrational numbers go on and on forever**, and never repeat.

You go back to being a flower.

Since you’ve just learned that **an angle defined by a rational number gives you a lousy distribution**, you decide to see what happens when you use an angle defined by an irrational number. Luckily for you, some of the most famous numbers in mathematics are irrational, like **π** (pi), **√2** (Pythagoras’ constant), and **e** (Euler’s number). Dividing your circle by **π** (360°/3.14159…) leaves you with an angle of roughly **114.592°**. Doing the same with **√2** and **e** leave you with **254.558°** and **132.437°** respectively.

Great success. These angles are already doing a much better job of dispersing your seeds. It’s quite clear to you that **√2** is doing a much better job than **π**, however the difference between **√2** and **e** appears far more subtle. Perhaps expanding these sequences will accentuate the differences between them.

It’s not blatantly obvious, but **√2** appears to be producing a slightly better spread. The next question you might ask yourself is then: is it possible to measure the difference between the them? How can you prove which one really is the best? What about Theodorus’, Bernstein’s, or Sierpiński’s constants? There are in fact an infinite amount of mathematical constants to choose from, most of which do not even have names.

Numbers can either be rational or irrational. However **some irrational numbers are actually more irrational than others**. For example, **π** is technically irrational (it does go on and on forever), but it’s not exceptionally irrational. This is because it’s approximated quite well with fractions – it’s pretty close to 3+1⁄7 or 22⁄7. It’s also why if you look at the phyllotaxis pattern of **π**, you’ll find that there are 3 spirals that morph into 22 (I have no idea how or why this is. It’s pretty rad though).

Generating a voronoi diagram with your phyllotaxis patterns is a pretty neat way of indicating exactly how much real estate each of your seeds is getting. Furthermore, you can **colour code each cell based on proximity to nearest seed**. In this case, purple means the nearest neighbour is quite close by, and orange/red means the closet neighbour is relatively far away.

Congratulations! You can now empirically prove that *√2* is in fact more effective than **e** at spreading seeds (**e**‘s spread has more purple, blue, and cyan, as well as less yellow (meaning more seeds have less space)). But this begs the question: how then, can you find the most irrational number? Is there even such a thing?

You could just check **every single angle between 0° and 360°** to see what happens.

This first thing you (by which ‘you,’ I mean ‘I’) notice is: holy cats, that’s a lot of options to choose from; how the hell are you suppose to know where to start?

The second thing you notice is **that the pattern is actually oscillating between spokes and spirals**, which makes total sense! What you’re effectively seeing is every possible **rational** angle (in order), while hitting the **irrational** one in between. Unfortunately you’re still not closer to picking the most irrational one, and there are far too many to compare one by one.

Fortunately you don’t have to lose any sleep over this, because there is actually a number that has been mathematically proven to be **the most irrational of all**. This number is called **phi** (a.k.a. the Golden/Divine + Ratio/Mean/Proportion/Number/Section/Cut etc.), and is commonly written as **Φ** (uppercase), or **φ** (lowercase).

It is the most irrational number because it is **the hardest to approximate with fractions**. Any number can be represented in the form of something called a continued fraction. Rational numbers have finite continued fractions, whereas irrational numbers have ones that go on forever. You’ve already learned that **π** is not very irrational, as it’s value is approximated pretty well quite early on in its continued fraction (even if it does keep going forever). On the other hand, you can go far further in **Φ**‘s continued fraction and still be quite far from its true value.

*Source:*

*Infinite fractions and the most irrational number: [Link]*

*The Golden Ratio (why it is so irrational): [Link]*

Since you’re (by which ‘you’re,’ I mean I’m) a flower (by which ‘a flower,’ I mean ‘an architecture student’), and not a number theorist, it’s less important to you why it’s so irrational, and more so just that it is so. So then, you plot your seeds using **Φ**, which gives you an angle of roughly **137.5°**.

It seems to you that this angle does a an excellent job of distributing seeds evenly. **Seeds always seem to pop up in spaces left behind by old ones, while still leaving space for new ones**.

Expanding the this pattern, as well as the generation of a voronoi diagram, further supports your observations. You could compare **Φ**‘s colour coded voronoi/proximity diagram with the one produced using **√2**, or any other irrational number. What you’d find is that *Φ* does do the better job of evenly spreading seeds. However **√2 **(among with many other irrational numbers) is still pretty good.

If you were to plot a range of angles, along with their respective voronoi/proximity diagrams, you can see there are plenty of irrational numbers that are comparable to **Φ** (even if the range is tiny). The following video plots a range of only **1.8°**, but sees six decent candidates. If the remaining **358.2°** are anything like this, then there could easily well **over ten thousand irrational numbers** to choose from.

It’s worth noting that this is technically not how plants grow. Rather than being added to the outside, **new seeds grow from the middle and push everything else outwards**. This also happens to by why **phyllotaxis is a radial expansion** by nature. In many cases the same is true for the growth of leaves, petals, and more.

It’s often falsely claimed that the **Φ** shows up everywhere in nature. Yes, it can be found in lots of plants, and other facets of nature, but not as much as some people mi

ght have you believe. You’ve seen that **there are countless irrational numbers that can define the growth of a plant in the form of spirals**. What you might not know is that there is such as thing as the *Silver Ratio*, as well as the *Bronze Ratio*. The truth is that there’s actually **a vast variety of logarithmic spirals** that can be observed in nature.

*Source:*

*The Silver Ratio & Metallic Means: [Link]*

A huge variety of plants have been observed to exhibit spirals in their growth (~80% of the 250,000+ different species (some plants even grow leaves at 90° and 180° increments)). **These patterns facilitate photosynthesis, give leaves maximum exposure to sunlight and rain, help moisture spiral efficiently towards roots, and or maximize exposure for insect pollination**. These are just a few of the ways plants benefit from spiral geometry.

Some of these patterns may be **physical phenomenons**, defined by their surroundings, as well as various **rules of growth**. They may also be results of natural selection – of long series of **genetic deviations** that have stood the test of time. For most cases, the answer is likely a combination of these two things.

In some of the cases, you could make an compelling arrangement suggesting that these spirals don’t even exist. This quickly becomes a pretty deep philosophical question. If you put a series of points in a row, one by one, when does it become a line? How close do they have to be? How many do you have to have? The answer is kinda slippery, and subjective. A line is mathematically defined by an infinite sum of points, but the brain is pretty good at seeing patterns (even ones that don’t exist).

M.C. Escher said that *we adore chaos because we love to produce order.* Alain Badiou also said that

This is the very firs experiment I did in DS10, October 2012. Even if I was unable to find an architectural application, i still find the interference colour patterns to be beautiful images, so I’m posting them here, hoping they will inspire someone else.

Thin-film interference occurs when incident light waves reflected by the upper and lower boundaries of a thin film interfere with one another to form a new wave. Check out the wikepedia article: http://en.wikipedia.org/wiki/Thin-film_interference

Three great BBC documentary films by Adam Curtis which help to understand our unit’s agenda: From Ayn Rand and Buckminster Fuller and the birth of the Californian Ideology, Ecology, Eco-Systems, Systems Theory and Cybernetics to George Price, Richard Dawkins and the Selfish Gene, see how the concept of “network” and “nature” has evolved as an ideology through modern times.

*All Watched Over by Machines of Loving Grace *is a series of film about how humans have been colonized by the machines they have built. Although we don’t realize it, the way we see everything in the world today is through the eyes of the computers. It claims that computers have failed to liberate us and instead have*distorted and simplified our view of the world around us*.

**1. Love and Power**. This is the story of the dream that rose up in the 1990s that computers could create a new kind of stable world. They would bring about a new kind global capitalism free of all risk and without the boom and bust of the past. They would also abolish political power and create a new kind of democracy through the Internet where millions of individuals would be connected as nodes in cybernetic systems – without hierarchy.

**2. The Use and Abuse of Vegetational Concepts**. This is the story of how our modern scientific idea of nature, the self-regulating ecosystem, is actually a machine fantasy. It has little to do with the real complexity of nature. It is based on cybernetic ideas that were projected on to nature in the 1950s by ambitious scientists. A static machine theory of order that sees humans, and everything else on the planet, as components – cogs – in a system.

**3. The Monkey in the Machine and the Machine in the Monkey**. This episode looks at why we humans find this machine vision so beguiling. The film argues it is because all political dreams of changing the world for the better seem to have failed – so we have retreated into machine-fantasies that say we have no control over our actions because they excuse our failure.

Adam Curtis is a documentary film maker, whose work includes The Power of Nightmares,The Century of the Self, The Mayfair Set, Pandora’s Box, The Trap and The Living Dead.

After posting about the book explaining basic concepts of computational design,** The Nature of Code **by Daniel Shiffman, I thought it would be helpful to convert all the example into Grasshopper files. Well here you go: **Jake Hebbert **has done it on youtube, exciting tutorials using python for Grasshopper. Here are couple example of tutorials extracted from **Jake’s youtube channel:**

**Walker:**

**Walker02:**

**Bouncing Balls:**

**Gravity between movers:**

Here is the book that I kept mentionning in the tutorial: ** The Nature of Code** by Daniel Schiffman

The book explains many algorithm that attempt to reproduce natural systems (including swarms and fractals) using **Processing**, the java-based scripting interface.

You can download the book and make a donation or buy the hard copy. Try some examples, register to the **Processing forum** and to **StackOverflow.com**. Ask for help on the **Processing IRC Channel**.

For some example, you will need to need to download the **Toxiclibs **library and you might want to use the **Eclipse IDE** to speed up your workflow. You can also follow the great Plethora-Project.com tutorials by Jose Sanchez.