Thank you all for coming.

My name is Anna.

I'm a freelance JavaScript developer from Berlin.

But my background is actually in computational linguistics.

Computational linguistics is the signs of looking at natural language.

So the stuff that we human speak in a mathematical way trying to find patterns and rules, um, to do awesome stuff with it.

Um, and this is what inspired this talk.

I want to talk about something called the Algorithmic Beauty of plans.

So when people talk about mathematical aspects of plans on the beauty of nature, you usually see those kind of images show up circular shapes with easy the recognizable repeating patterns.

Sometimes he even see if you were not.

She's spiral drawn on top of it to indicate the Golden national somewhere in the plant.

Uh, whether this is true on that, but this is what people usually talk about.

However, in this talk, I would like to give you another approach to seeing the mathematical.

And I go with Mickle beauty of plans.

And this approach actually starts with the human language.

So a common thing between people off all cultures in the world, it's that they use language to communicate, while those languages very wildly, quietly, there seems to be a common feature connecting them.

So, uh, humans speak to each other using languages.

They have different structures, different words.

But there's some similarities, and this is what linguistics is about.

So to give you an introduction to how we linguist look at language, Um, I say, Let's have a look at a couple of English sentences and see if we can find out what makes them sentences.

So look at this sentence.

It's called America reviewed Peter's pull requests.

That sounds like a wonderful English sentence to us.

However, if we rearrange the word will request Marika, Peter's reviewed doesn't sound like an English language.

So if you have another native language than English or German, maybe a non European language this what structure might make sense to you.

But for English and German speakers, it usually doesn't.

So another sentence that isn't really ascendance is something like Jessica talks about.

There's something missing in the English language, so our brain gives us this kind off error message when we listen to that and you love with every message.

But actually we can observe something like this so when linguist tried to figure out what makes a sentence.

Grammatical four speakers.

They have a couple of techniques techniques to check that, um, one technique uses eye tricking.

So when we read a sentence like this, um, the test subject eyes go back to the front of the sentence furiously looking for that missing information you even can put on then e k g to measure the brain waves.

Thank you.

See that there's a spike in it when it sentences under medical.

So this is really interesting.

Um, the first sentence had a word order that we perceived as non grammatical.

This sentence is seems to be missing a word, but then their sentences where l brain doesn't throw an error message in a grammatical way, for example, of this sentence colors, green ideas sleep furiously.

It is a perfectly valid English sentence, but it doesn't make any sense.

So we laugh about that.

But we don't get that much.

It's thrown.

Um, so they seem to be some rules that we can break and still maintain an English sentence in some that we can't, um and we want to figure out what is it that makes a sentence that developed English sent into that case.

The fun thing is, it's grammar.

Um, some of you had grandma studies in school on their return, some basics about their native language.

Some didn't in linguistics.

A gram is just a set of structural rules that tell us how a sentence a phrase, so sometimes even the word may be composed.

So it has nothing to do with so called press prescriptive grandma, where we say, What rules make a nice sentence?

And if you say that your teacher, if you say the other one, your teacher will say it's wrong.

But really just figuring out what throws the error messages and or a brain and what does?

Um, grammar has always been a part of learning a language.

So even 100 years ago, when people were studying different languages, they looked at the grandmother, looked at the word order, um, to figure out what is a good sentence and whatnot.

Looking at grammar and language is from mathematical angle actually started happening in the fifties.

So for our approach right now, we just agreed that the ground was a set of rules.

Hell, words maybe put together, um not nice sentences, not educated sentences, but just developed sentences.

Um, when I said it started in the fifties, it actually started mainly with this person.

It's called known Trump Ski.

He used to be a very important theoretical linguist.

Now what?

I see a switch to politics and, uh, philosophy.

But he laid the groundwork for all mathematical approaches.

Two languages.

Um, it went this far over that we actually call this kind of grandma Chomsky grandma or Trump's key systems.

Um, and in a very short, uh, summary, he says that the grandma's a type of rewriting system that contains rules that tell us how words maybe put together to form a sentence.

So what is the rewrite system?

It might sound complicated, but actually just search, search and replace symbols.

We, for example, have rules like this.

It's an s and a ronin, a newbie.

And that just means every occurrence off the symbol on the left hand side are this error.

So the S is replaced with a baby, not the other way around.

Yes, it's written here that you may be using already those kind of rewrite systems.

If you use auto former dust like pretty that replace every double quote with single quotes or the other way around.

This is just a rewrite rule.

More complex room would be the 2nd 1 So, um, only if the symbol A appears to the left of be replace it with C or even the 3rd 1 If A and B appeared together, replace them with C.

Um, and this is just This is hella rewrite.

Rule works.

It's it's simple.

Replace one thing with another, according to some logic.

And with us, we already can build as a grandma for human language.

So this is a simple sentence.

It works.

Nobody gets an armistice room.

Jessica talks, and we have two types off words in the sentence.

One is called a noun.

Jessica is a noun.

It's a word that identifies a person, an animal, a place, a thing or an idea.

Um, the other thing is talks.

And is this a verb?

The verb.

It's one of the main parts off any sentence or any language.

If you will always find works in languages, they're like functions.

Jessica talks.

Uh, talking is kind of a function of the object.

Jessica and they really tie the information together that we're having like a really real sentence or question can't work without a work.

Of course, some exceptions, but in general the verb is the important thing.

Um, this is how important these action parts of speech are.

The probe's signals in action and accordance or state of being, whether mental, physical, mechanical, Uh, somehow there's an activity expressed so a simple rule for English sentence would be.

A sentence is a noun full of fiber, so we would have a record like this have signed a symbol for ascendance.

I could replace them with mounted verb, and this allows us some simple sentences like Jessica talks or Florencia dances.

Um, but we reached the borders of our grandma pretty fast, was just the dog barks or Florencia dances with a broomstick.

And in logistics, we call that grandma not expressive enough.

So we need to add more rules, too.

Form a complete grammar.

So when we have a sentence like Jessica talks about machine learning, we again see Maur announce.

We see the verb that before, and we have a new word about which we call a proposition.

Um, this is the work of a word form that links announce pronouns and phrases together in a sentence, so to create a new meaning.

So we remember this rule in that sentence is a noun and a verb.

We say, Okay, that's not enough.

Now we can come up with something more expressive.

Um, another word phrase is coming to the grammar phrases that just groups, um, off words that form a specific unit in a sentence.

So known phrase, it's not just a noun like Jessica can also be noun an article like the dog.

And the verb phrase is not just the verb, but all the information that belongs to it.

So talks about machine learning.

Um, there are some elements to form a grammars that we use a so called non terminal systems symbols.

Now, in verb and proposition L A word forms terminal systems that symbols that are actual words and a set of rules.

Um, when we have a couple of rules, we can use them one after the other.

So we start with the S, we re expanded to Nantes, raise and drop raise.

We expanded to now, and we're price and so on.

You see that there's a kind of tree structure emerging from it and non terminal systems just appear in the notes and the terminal symbols that we learn that at one point all the leaves of the tree.

Um and, um, this is a simple grammar, applying the production's you can see on the right hand side how that works.

And with that very simple grammar, we can actually already form quite a lot of sentences.

So the Children talk about Jessica is developed senses and just are 4 to 6 program.

Our Children sing with joy, um, Children sing et cetera.

And now the cool thing of Grandma's comes into play.

We have, um, can generate sentences with it.

And if we write a hologram in a specific way, we can have an infinite amount of sentences.

Was just a minute set of rules, which is pretty cool.

Um, so if we just at something that we call objectives, um, so, uh, the Children sing the big Children sing the big, funny Children, seeing the big, funny, lovely Children, saying You can see that we can create an infinite amount of sentences just by adding the rule that we love objectives now, Um, and this is cool because we seem to be able to harness.

Uh, an Internet group of sentences was just a few rules.

Well, this was a very quick run through how former grandma's for natural languages work.

So they get the idea, um, and the knowledge that you need for the nice things with a plant, Um, just a heads up.

If you ever are interested in that, you will see that these small grandma's are just not expressive enough.

These for so called regular grandma's um, but there's something called context re grammars, or context sensitive grimace that allow for more complex sentences that might escape the simple rule set.

So now, to this to the plants, there's another lovely person called RST Lindenmeyer.

It's actually a theoretical biologist on, and there's a nice origin story.

How old this works together.

He was a teaching at the university, and he was working on describing the growth off LG actually.

So the plants in the water and there was thinking a lot about that, and he was passing a room where they were teaching theoretical computer science and talking about the language of Grandma's.

So what kindof set off sentences?

It's a specific grandma producing and, uh, in theoretical computer science.

It's denoted with L.

G.

And he just heard Oh, what I'm talking about algae algae.

That seems to be something that's my interest, because I'm looking at those plans and he went into the class, um, not knowing that he was mistaken.

But from that class he was watching, learning about Grandma sent rules.

It was actually able to develop a theory based on that to describe plant growth.

So, um, these systems that he developed our so called L Systems, Alden Meyer Systems and the Day hey describe the behavior of plant cells to model the growth process of plant development.

It started with the L G, but later it was more complex organisms.

And when you look at those plans, you see that there's some kind of structure to its some kind of rule.

It's not just based in the wild, Um, and it's tree.

And, uh, having a grammar gives us actually the possibilities of to describe something like this.

This is a simple plant.

It grows, um, and when we watch the different stages off the plant growth, we actually see that there's some sort of system for it.

There's also some sorts off repeating elements.

So we have a size one.

Leave somewhere with a stem were size to leave or size three leave.

So, from the first of the second plan, the size one leaf has been replaced by two sides.

One leaves the 2nd 1 The two sides of one leaves have been replaced by a stem and the two sides one lease.

Ah, so we can actually already see that there's some kind of rewriting could be going on.

Um, when we talk about Lindenmeyer systems, we have to, um, main elements of our grandma.

So first we had those terminals, symbols and non terminal symbols and inland my assistance.

We just have an axiom.

It's kind of the seed of the plan.

So the starting work, so to speak, and replacement rules that describe how are plans grow.

And in the linguistics, Grandma, we applied one rule after the other, and in my systems, the rules actually applied ultra giver.

So on the first step, we have our seed, our s.

We have a rule that says, replace the s with Ellen.

This Okay, we do that and then we haven't l that says replace it with S S r.

And we have an s again.

So now the rule for the S and the L will apply as well.

Um, every stage off rule application is actually a different plan and develop plant.

So first with seat, then we have one leave when we have a couple of leaves.

And then in the end, we have a tree.

Oh, and you see if you, um right the rules the right way, the words the trees can be pretty big Pretty soon.

So to summarize, it's a revised system.

We have to see it in the beginning.

All rules applied at once and every step is a, well, a word or plant.