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Fractal planting patterns yield optimal harvests, without central control (phys.org)
255 points by dnetesn on June 10, 2017 | hide | past | web | favorite | 70 comments

This reminds me of something from Sam Bowles's "Microeconomics":

Like the overnight train that left me in an empty field some distance from the settlement, the process of economic development has for the most part bypassed the two hundred or so families that make up the village of Palanpur. They have remained poor, even by Indian standards: less than a third of the adults are literate, and most have endured the loss of a child to malnutrition or to illnesses that are long forgotten in other parts of the world. But for the occasional wristwatch, bicycle, or irrigation pump, Palanpur appears to be a timeless backwater, untouched by India’s cutting edge software industry and booming agricultural regions. Seeking to understand why, I approached a sharecropper and his three daughters weeding a small plot. The conversation eventually turned to the fact that Palanpur farmers sow their winter crops several weeks after the date at which yields would be maximized. The farmers do not doubt that earlier planting would give them larger harvests, but no one the farmer explained, is willing to be the first to plant, as the seeds on any lone plot would be quickly eaten by birds. I asked if a large group of farmers, perhaps relatives, had ever agreed to sow earlier, all planting on the same day to minimize losses. “If we knew how to do that,” he said, looking up from his hoe at me, “we would not be poor.”

The key takeaway from that is the difficulty of social organization. The first proponent of early sowing will be viewed as seeking to gain some private advantage precisely because poverty creates an economic incentive to maximize private advantage. Some open source proponents overcame this reluctance in the 1980s with the Stone Soup metaphor.

Could you please expand a little on the open source / stone soup metaphor part? I couldn't find anything on Google.

It was part of the original documentation for Fractint - software for generating Mandelbrot and Julia sets, substantially expanded later on - which was many people's first exposure to the concept of open source.

GNU was already operational but ineffective, which was why Linux (which was more focused on something that worked and less on maintaining ideological purity) took off like a rocket shortly after Linus released it.

I know you know your history and I know that you're smart because of the many many comments of yours I've read over the years but I have to disagree with you.

The whole point of GNU was to make a free UNIX. They logically started with the tools to do this. Editor, then compile tool-chain, standard library, user-land tools, … the kernel was to come eventually. But kernels are _hard_, not necessarily because writing a pre-emptive scheduling system with virtual memory is difficult (it is) but because 50% of the OS is drivers and for that you need hardware documentation. Besides a kernel ideally needs CPU support.

The i386 was the first mass market cheap CPU to provide a large (virtual) addressable space, memory isolation (rings 0..3), and so on. This was when Windows took off if you'll remember and when Novell was able to write a decent networking server, and Xenix, and OS/2, and I even remember buying a book that presented the source code for a 32-bit OS on i386 that I bought and marvelled at and lost somewhere on my travels.

Linus wrote Linux _at the right time_ for the i386, and built upon GNU. He famously said that it was a small project, not big and fancy like GNU -- you can Google the exact quote. Also, Linux uses GPLv2!, the socio-legal hack that Stallman and co. came up with, so Linux was _doubly_ dependent on the fruits of GNU. Why do you think Stallman and many others to this day want us to call our systems GNU/Linux? So I disagree -- though lacking a kernel, GNU provided a hell of a lot so I wouldn't call it ineffective just because they didn't manage to make a kernel.

It is true that Linus is more pragmatic than ideological. Having said that I think it is distro vendors that package the kernel with binary blobs, I'm not sure if blobs come with the kernel but I'm totally open to correction on this front, it's been a very long time since I looked under the hood! But I reckon Linux's success was due more to Linus's engineering skills, social skills, coding skills, taste, building on the work of Intel, PC architecture, and GNU.

Peace out anigbrowl! :)

Sorry about leaving this excellent comment without a reply. I completely agree, and overstated things by saying GNU was moribund.

The great thing about Linux was not just it was accessible and so on, but that it fit on (iirc) 4 1.44mb floppy disks and so you could get it up and running in under an hour.

For anyone who's still as confused as I am, apparently the connection between Stone Soup and open source is that the group who developed Fractint (one of the first open source programs and still used today) was called the Stone Soup Group.

Background from the Fractint website:


The stone soup is explained in wikipedia. https://en.wikipedia.org/wiki/Stone_Soup

Thanks. I read that before I posted my comment but there's nothing about stone soup / open source there (or on Google afaict), so I thought I was missing something specific.

That wikipedia article does contain this:

> Dungeon Crawl Stone Soup a computer game which expanded on an abandoned project using contributions from many different coders;

This is how visitors from other planets look at us in regard to resource distribution on earth and space exploration.

Game theory should be taught in high school.

If we discover that aliens actually exist and present an existential risk then the game will change. We'll effectively be drafted into team Earth.

So, your prediction for Game of Thrones is that the White Walkers will bring about peace and unity to the competing factions of the Seven Kingdoms ;-)

That was the exact thought I had when the White Walkers made their first appearance in the book!

Little reckoning the far wider existential threat of GRRM abandoning altogether and the universe simply ceasing to exist ...

The "aliens watching us" meme is overused and tiring to see. The aliens could actually be unable to perceive their existence. Or their civilization could be an ancap paradise/nightmare. Or a an authoritarian, communist dystopia. Or they could be nuanced enough to understand why things ended up happening the way they do.

Whatever it is they are however, they're doubtless more advanced if it's they watching us.

That story makes no sense. If those farmers of Palanpur can not agree to plant all together at the right time, how come they manage it several weeks later, or ever?

At some point, the individual losses from planting later become larger than the losses from birds. Then somebody plants, and then they all do. The first farmer to plant loses more to birds than everyone else, but less than he would by delaying more.

Also, I think their will be time limit. Like you have to sow in a week or you loose the window for the winter corp. And you know everybody will sow in that last weeks. I think there is some game theory around this.

I didn't understand:

1. how they didn't have pest problems if they planted in fractal patterns

2. but they did have pest problems if they didn't plant at the same time

Could someone kindly explain that in a little more depth?

> When farmers are planting at different times, pests can move from one field to another, but when farmers plant in synchrony, pests drown and the pest load is reduced.

The strategy is that if there are several fields planted for the same amount of bugs, each field receive less bugs than if it was the only one planted (on the contrary, if they were planted one after an other, the whole bug population would just jump from field to field).

Thanks, I thought when it said drown it literally meant something to do with water but this makes a lot of sense now.

Yes, they meant literal drowning of bugs when the field is flooded with water, which is one of the stages of growing rice. Bigger the area flooded at once, lower the chance for the average bug to escape. Fractal pattern arises as a trade-off because water supply is limited - if it wasn't for that they would probably just flood ALL the fields at once.

So what's going to happen with coordinated planting long term? Will the bug population expand? Does the narrower window when there are crops available negatively affect the bug population compared to a staggard planting?

Basically they are using the https://en.wikipedia.org/wiki/Predator_satiation strategy to reduce loses.

Its actually that planting "in synchrony" reduced pests. Balancing that with limited water supplies resulted in the fractal pattern, which created close to an optimal yield.

I fail to see how the planting patterns are fractal. A fractal pattern is one which repeats itself at different scales. I realize that the repetition does not need to be exact but I don't see how there is any at all in this situation.

Actually, that is only one type of fractals. Perfectly self similar patterns like the Triforce or Sierpensky triangle are used as toy models for learning . Typically, fractals in nature are not self similar(Branching of your blood vessels for example) . Mandelbrot developed fractal geometry as a way to model nature that captures roughness. It was kind of a rebellion against calculus, where if you zoom in eventually you get smoothness. It's funny that many people think that only self similar patterns are fractals when his desire was to get away from idealized models towards more pragmatic ones

EDIT: I'm actually just learning about fractals, so I'm certainly no expert, but I'm excited to share what I've learned so far.

Look at a line, square, and cube in 1, 2, and 3 dimensions respectively. If you scale down each by 1/2 in all its dimensions, you need to look at how much of the "mass" (for lack of a better term is scaled down

If you cut a line in 1/2, it's mass is scaled by 1/2 as it takes 2 one-half length lines to make the original line.

If you scale a square down 1/2 along all its dimensions, you break into/scale it down into 4 smaller squares, it's mass scaling factor is 1/4....scaling a cube down 1/2 along all its dimensions (1/2)^2 breaks it into 8 smaller cubes...it's scaling factor is 1/8 and you can see the progression here. (1/2)^3. (I imagine a tesseract/hypercube has a scaling of 1/16 as it is the 4D analogue of a cube) The exponent represents the concept of dimension and this is how you can have non-integer dimensions.

So, back to the Sierpenski triangle or triforce example. Let's scale it down 1/2. When we do that, we know we get 1/3 the "mass" of the original since there are 3 triangles contained in the larger triangle at each level. The dimensionality is then (1/2)^x = 1/3 where x is the dimensionality. We rewrite this as log 3 base 2 which gives it a dimensionality of ~1.585.

And that is the definition of a fractal, a shape with a non-integer dimension which gives the shape roughness at every scale. I don't quite understand the more technical definition, but hopefully this helps!

Note, you cannot use length or area as a measurment for a scaling factor, as the length would be infinite and area would be 0. Also, I say mass because the more correct concept is difficult for me to explain without a whiteboard, but basically, it has to do with putting the fractal on a 2d grid, scaling it, and seeing what the ratio of boxes touched is. See, told you I'm bad at explaining it :D

I forgot to add that fractal dimensionality is a clear differentiator between natural and man made things. So, it does make some sense to separate the natural from the synthetic.

Off topic, but does anyone know how this would affect the Fermi Paradox if aliens produce technology inherently fractal in nature?

I did enjoy it, if you can't tell from the content of my original post. I never quite knew what fractals were until yesterday afternoon. After 30 minutes of youtube, I'm explaining it to someone else, although at a 10 yr old's level.

There's no One True Definition of what it means to be fractal, but a lot of working mathematicians use the criterion that a space's Hausdorf dimension is not equal to its topological dimension. Oftentimes (but not always), the Hausdorf dimension will be fractional, which is where the word comes from. Self-similarity is an easy way to satisfy that requirement in a way that's easy to explain, but it's far from the only way.

I was under the impression that the fractal dimension must be greater than the topological dimension for the space to be a fractal.

And that the fractal dimension is usually equivalent to the mincowski dimension (the limit of the area measured by finite boxes as the size of the boxes grows arbitrarily small) and hausdorf dimension (the limit of the perimeter as measured by an aproximting polygon with equal length sides as the number of sides grows arbitrarily large) along with others.

Yea, in metrizable spaces, those statements are equivalent.

Something as simple as a contour map could be thought of as intrinsically fractal. It isn't as mathematically rigorous as the fractals we are used to seeing described as such, but it fulfils the criteria.

I agree; the term is drastically misused in this context. Planting is simply 'varied'.

There is an agent-based model of Balinese irrigation written in NetLogo here: https://www.openabm.org/model/2221/version/3/view

This looks very interesting from a regulation point of view, as a potential way to bring greedy self-interest into alignment with national/international social interest. I wonder what scenarios could be given a "pest tax", to alter the dynamic from a tradgedy of the commons to a cooperative/competitive optimum?

The classical solution to the tragedy of the commons for rivalrous goods is propertization. It's the logic behind contemporary land rights, some very successful commercial fisheries management (north west Atlantic), and emissions auctions in the US (SOx and NOx implementation - but notably not the proposed carbon, which has other wierd factors bolted on)

That's terribly limited though, since it basically relies on a land grab, and people who come along later are out of luck.

That's why you introduce a land value tax. As the supply of interested parties increases, so too does the demand and therefore the value of the land. This has several effects:

1) incentivizes unproductive land owners to sell

2) incentivizes productive land owners to seek tenants

3) generates public revenues to offset negative externalities

That never seems to get mentioned at the time the commons are privatized, only in salons later on. Also, it's rather hard to build capital improvements on fisheries, and correspondingly this does nothing for the preservation of wilderness. which is a problem that privatization is supposed to solve but frequently doesn't.

Yes but the rentier class (our overlords) don’t like LVT.

How does that apply to rolling auctions?

There's plenty of science against (20th century) top heavy / top down control. The issue seems to be: the current power holders admitting their model is flawed; and those being managed realized they'd be better off without "leadership."

I believe ecology has to be turned into a strong economic factor if we want anything to happen in its favor. Assuming political cooperation, the easiest way I see is to just slap a tax on any and all polluting emissions. That's very much top-down and seems very useful.

> top heavy / top down control

Could you characterise what is meant by this?

I know that achieving some objective 'X' may not be amenable to regulation which says 'you must do X'; but regulation may (in some circumstances, with sufficient thought) alter the situation's dynamics such that greedy self-interest in that environment just-so-happens to coincide with causing 'X'.

What better alternatives are there to "top down control"; do you mean a "vote with your wallet" sort of 'bottom up' pressure?

Centralized, as opposed to decentralized. I would say these farms/farmers are decentralized. There's no gov agency, with some academia pencil pusher in some removed city overseaing them. They've figured it out. And they will continue to do so.

p.s. Team of Teams (book) does a great job flying to decentralized flag.

Not quite. There's plenty of examples in nature of automatons executing simple behaviors without an overseer that lead to tremendous complexity and efficiency.

However, we only see the successful emergent phenomenon, not the failed ones. Also, to this day we can not make accurate predictions of inherently chaotic systems.

So, while a bottom up sysytem may optimize, exactly whatt it optimizes is impossible to discern.

Well. Yes. But I didn't say always. Only that it is (often?) very possible to find solutions in a local decentralized sort of way.

Private property and profit motive are obstacles.

If you don't support neoliberal fantasies, your comments probably aren't welcome here.

Not really; they're exactly what I meant by "greedy self-interest".

Now how can I apply this to Dwarf Fortress?

That's an absolutely valid question that doesn't deserve to be downvoted. Generalizing these insights for deployment is absolutely a problem worth solving.

Haha, people can be such assholes sometimes.

Dwarf Fortress doesn't currently have crop pests, but it's reasonable to assume it will within a decade. Tarn plans to spend the rest of his life working on it.

Dwarf Fortress is a game about decentralized, organized planning so once pests are added we'll see pages and pages of discussion about the best way to plan your fractal farm.

Sure, I was being half serious but c'mon people have a sense of humor.

TLDR; Locally collaborative greedy planting strategy leads to globally optimal results and looks like a fractal from above. Mind == Blown.

this is very interesting, wondering the principle applies to societal organization and current reversal trends on globalization (mono-culture) and weakening of international 'controlling' organizations.

Actually this depends on a monoculture as it is an adaptation to the life cycle of the rice (paddy) plant and its water requirements. If different farmers were growing different crops the requirements would vary.

Can anyone find sample satellite imagery that illustrates the fractal patterns? I didn't see any in the article or with a quick google search.

Fractal doesn't appear in the paper. I'm not sure where phys.org gets the word fractal from.

Here's some figures which might help with satellite image searches.


Is this a form of emergence?

Yes... both profs are external sante fe institute members. That's kindof their chorus.

Can you recommend a book or two on emergence? I've seen it mentioned. It intrigues me. But I haven't been able to find anything sold for going deeper. TIA

First read "more is different". Solid state physicists were first to pioneer in this field: http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72mo...

There's a very light book by some modern author that's not terrible: Emergence: The Connected Lives of Ants, Brains, Cities, and Software https://www.amazon.com/dp/0684868768/ref=cm_sw_r_cp_api_3Wxp...

If you want to really dig in though you need some math: Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems (World Scientific Lecture Notes in Complex Systems, Vol. 2) https://www.amazon.com/dp/9812388036/ref=cm_sw_r_cp_api_.Yxp...

Final suggestion is most of the stuff is online at different professors websites. Warning: the field is full of meaningless fluff too, and there's a lot of qucks mixed in with genuinely interesting science.


These insights will be useful for my political project.

so: monolithic frameworks vs loose coupled components?

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