# As you can perfectly see, I'm a strange-looking tree. How old am I?

As you can perfectly see,

I'm a strange-looking tree.

I grow over generations,

There's no trick, do not fret,

what you see is what you get.

I can go on and on, time permitting,

but even I had a beginning.

How old am I?

Hint 1

Watch it grow, but do not be fooled by the title of the video. "Iteration 11" is referring to the 11th L-System I've uploaded to YouTube, not anything inherently related to the L-System itself.

Hint 2

Hint 3

An L-System begins with an axiom.

Hint 4

Use my self-similarity as a guide.

Great tree,

your age is the number of iterations it took to generate you. You are a recursive fractal tree, generated via a L-system, and you have no life other than when you are generating or have stopped generated, at each step of generation your age being the number of iterations. Your age cannot be measure in human time scales like seconds, minutes, hours etc because it depends on the processor speed, generating speed etc etc etc (a lot of factors). But what remains as a valid invariant age for you is the number of iterations it takes to generate till some stage.

As you can perfectly see,

I'm a strange-looking tree.

Just a strange looking fern diagram using L-system

I grow over generations,

L systems almost always grows and never removes. Same case here.

There's no trick, do not fret,

what you see is what you get.

Obviously there is no trick. it's just a finite character rewriting system following basic rules of formal language and grammar systems. And what is being drawn is what we get as a diagram, which is basically a mapping from a subset of the words of the language to a geometric movement.

I can go on and on, time permitting,

L-systems go on generating if not given an explicit stop condition like number of iterations and such. This is because it generates infinite sequences of words from the available words of the language.

but even I had a beginning.

All L-systems start from a axiom, which is basically a word from the language, to be modified via the derivation defined. Your start is $$Y$$ and derivation is $${X → X[(-FFF)][(+FFF)]FX}{Y→YFX[(+Y)][(-Y)]}$$.

How old am I?

6 iterations. Did the L-system myself xD. I am sorry.

• You're on the right track! You've got everything but the age correct! May 7 '20 at 16:14
• Am I correct on the bound? May 7 '20 at 16:15
• The last bound you mention is closest, and it is nearly correct. May 7 '20 at 16:17
• The last bound? 1340-268? May 7 '20 at 16:17
• rot13(Lbhe cre frpbaq vgrengvbaf vf pybfr gb gur ahzore bs vgrengvbaf sbe gur ragver gerr.) May 7 '20 at 16:20

Perhaps you are a

Family tree

Which would make you

About 200’000 years old - as long as humans have been around

As you can perfectly see,
I'm a strange-looking tree.

A family tree branches out from a beginning similar to the photo

I grow over generations,

The tree grows as new generations are born. It cannot go backwards (think that should be degradations?)

There's no trick, do not fret,
what you see is what you get.

You can look at a family tree and there is no trick to it

I can go on and on, time permitting,
but even I had a beginning.

As long as time allows, the human family tree will keep growing for as long as humans are around. Even the family tree had a beginning with the first human beings.

How old am I?

Humans came into existence about 200’000 years ago, which makes the tree the same age

• rot13 Guvf vf n ernyyl jryy gubhtug bhg nafjre, naq vs gur chmmyr jnf gur cbrz nybar, V jbhyq npprcg vg. Ernyyl, tbbq wbo. Nf fbzrbar genvarq va gur ovbybtvpny fpvraprf, V'z nyfb unccl gb frr lbhe nafjre ba gur beqre bs gjb uhaqerq gubhfnaq lrnef engure guna guerr gubhfnaq gb gra gubhfnaq lrnef. May 2 '20 at 1:52
• @Galen it fits the poem very nicely but definitely not the video, I certainly wouldn’t describe a family tree as iterative :P May 2 '20 at 1:58

Okay, so I'll try and have an attempt at this..., I think the answer is a

Recursive Tree

So,

Dating to the inception of recursion by the Greek mathematicians, that would be around 400 BC...so that's quite old.

Next,

Growing ever "generations", without suffering degradations, that's exactly what recursion does as it grows, also it may be noted that "generators" are closely related to recursive functions in programming and Computer Science, "generating functions" in Mathematics also bear a resemblance.

A sound justification for "I can go on and on, ....even I had a beginning"

Well, exactly ! A base case is all that, a recurrence relation or a recursive tree needs to keep on growing. For a simple example, one might refer to the simple Fibonacci Recurrence relation, F(n) = F(n-1) + F(n-2)...this will keep on growing alright, but the base cases, the "beginning" so to say, must be specified. F(0)=1, F(1) = 1.

They show the growth of Fractal trees, the bush fractal, and fractal trees can be created in programming languages using the concept of Recursion, a recursive relation or function to be precise that governs the growth or branching of the tree, So I believe even if you intended fractal trees to be the answer, recursion would be the principle at heart.

I am a strange looking tree.

looks like bacteria growing and evolving

I grow over generations.

Bacteria keep growing. One generation follows another.