Design: The Divine Proportion and natural sequences

[edprocoat]

I look at the Fibonacci tree and think I would cut off the entire left side down to the lower trunk just to begin with ...

ed

 

[bonsaiBlake]

The Golden ratio is a natural law which governs growth and development of structure for some plants. Because it is so prevalent in nature humans eyes are naturally attracted to things which follow its rules. Theres even an app to see how close your face is to being "perfect" to the rule. Its fascinating topic. Naka actually mentions it within the first 20pgs of Bonsai Techniques 1.

 

[qwade]

I look at the Fibonacci tree and think I would cut off the entire left side down to the lower trunk just to begin with ...

ed

And you would still be in sequence

 

[Vance Wood]

I look at the Fibonacci tree and think I would cut off the entire left side down to the lower trunk just to begin with ...

ed

OK____Who the heck designed the Fibonacci tree and what's the point of it? If it is a matter of poor choices, which is what this impossible tree presents, I would cut the thing down to the ground, start a fire and roast marshmallows. What are we supposed to be seeing and understanding. So far much of this is totally esoteric. If we are really being serious here someone pleas explain this one point with this one concept so that I can understand it.

 

[tmpgh]

OK____Who the heck designed the Fibonacci tree and what's the point of it? If it is a matter of poor choices, which is what this impossible tree presents, I would cut the thing down to the ground, start a fire and roast marshmallows. What are we supposed to be seeing and understanding. So far much of this is totally esoteric. If we are really being serious here someone pleas explain this one point with this one concept so that I can understand it.

I asked, pretty much, this same question and my response was that tree, which if anything complicated things rather than simplifying them. Show me a real tree, with some tape measures, illustrating the principle in action so that I can grasp it in a concrete way, and not in some theoretical one. The Fibonacci tree is... horrific to look at and if it is a model for what should be done, I'm sooner to burn my trees than follow those rules.

 

[qwade]

I guess you guys can't see the forest for the tree.

The diagram of the tree represents. what you would call ramification.

In nature, this ramification closely follows the fibonacci sequence. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems and so on--- as depicted in the tree you guys want to make firewood out of. The number to the right indicates the number of branches in that ramification.
Now as blake above noted the pattern of this sequence has been shown to be pleasant to the eye. Whether it be a tree or the face of a young lady. This is the point of the discussion as it pertains to bonsai.

This pattern of numbers is repeated many times in nature most notably in the pattern of flower petals as well as the spirals of seeds in a sunflower. It has been studied for millenniums. The ratio can even be seen in DNA

Is this a serious discussion?----absolutely!!! And to me a very interesting one. Its not for everyone. But if interested a good book to read is The Golden Ratio: The Story of PHI, the World's Most Astonishing Number. Kind of a hard read.
I am no professor so it would be hard for me to explain any further. You would need to do your own research. A very interesting ratio!

Oh and Vance if you measured the height from the floor to your belly button and then measured the the distance from your belly button to the tip of your head--- the ratio would be the "golden ratio"! go figure

 

[Vance Wood]

I asked, pretty much, this same question and my response was that tree, which if anything complicated things rather than simplifying them. Show me a real tree, with some tape measures, illustrating the principle in action so that I can grasp it in a concrete way, and not in some theoretical one. The Fibonacci tree is... horrific to look at and if it is a model for what should be done, I'm sooner to burn my trees than follow those rules.

Hallelujah, the King is not wearing any clothes, someone gets it------or in this case does not get it. I agree with you. If you get this and understand how it works and how it applies to bonsai you need to explain it else all you are doing is bull shitting as far as I and many others are concerned.

Too much of what goes on lately, not only in bonsai but other endeavors, has become esoteric in nature leaving the majority of us hoy-paloy floundering in darkness afraid to admit we don't understand. I don't mean to interject any contention into the thread but if all we are doing is posting up a bunch of high sounding ideas and concepts but can't------or wont--- explain simply, how this applies to bonsai, why are we doing this at all?

 

[tmpgh]

I guess you guys can't see the forest for the tree.

The diagram of the tree represents. what you would call ramification.

In nature, this ramification closely follows the fibonacci sequence. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems and so on--- as depicted in the tree you guys want to make firewood out of. The number to the right indicates the number of branches in that ramification.
Now as blake above noted the pattern of this sequence has been shown to be pleasant to the eye. Whether it be a tree or the face of a young lady. This is the point of the discussion as it pertains to bonsai.

This pattern of numbers is repeated many times in nature most notably in the pattern of flower petals as well as the spirals of seeds in a sunflower. It has been studied for millenniums. The ratio can even be seen in DNA

Is this a serious discussion?----absolutely!!! And to me a very interesting one. Its not for everyone. But if interested a good book to read is The Golden Ratio: The Story of PHI, the World's Most Astonishing Number. Kind of a hard read.
I am no professor so it would be hard for me to explain any further. You would need to do your own research. A very interesting ratio!

Oh and Vance if you measured the height from the floor to your belly button and then measured the the distance from your belly button to the tip of your head--- the ratio would be the "golden ratio"! go figure

First, if the tree in the pic is to represent a real tree or ramification, it should look like it. It looks ridiculous. If it looked like a decently ramified tree instead of impressionistic art crap, we could perhaps recognize it as a tree or ramification.

Is it a serious discussion? I think so. But, as Vance said, if we're just going to throw around terms and post up fancy charts, it isn't. Let's see a tree that actually looks like that in nature and another that actually looks like that in a pot and lets talk about if we think they are art or not.

 

[davetree]

Good luck getting your tree to conform to the golden ratio. Btw, that ratio exists in the petals of some flowers, not most, and certainly not all. Not all sunflower seeds either. Just some. Approximately.

 

[Alain]

Actually; Mozart lived in a world where "the rules" were everything, as did Bach. However; being really good at what you do tends to change the rules to allow for your artistry if you happen to be one of those individuals that does things that change the rules. Bach, solidified the Baroque style and understanding by taking that style from the Renaissance and moving it forward. He even changed the tonal structure to what we understand as the standard today. The well tempered scale system. Mozart took the Baroque and took it beyond and laid the foundation for Beethoven who laid the foundation for every thing to follow. All of the music we know and love today has it's foundation in the minds of these three guys and their music. Does that mean we should design our music to sound like these three duds? YES! Only in that we build on the previous without fear of the unknown before us. If this is not done the art will die.

I'm sorry Vance but this is how one could describe the work of some artist.
I'm pretty sure that when Mozart wrote music he just, you know, wrote music...

 

[tmpgh]

I'm sorry Vance but this is how one could describe the work of some artist.
I'm pretty sure that when Mozart wrote music he just, you know, wrote music...

That would be a drastic over simplification of things. There is no question that Mozart fully understood the rules, and that he very carefully picked and chose when to follow them and when to bend them and when to break them altogether. To say he just sat and magic happened... well, just not so. Great art requires great study, practice, skill, knowledge. It doesn't just happen. Mozart had the tremendous ability to instantly understand music in a way that most people cannot even after years of study. This doesn't mean he didn't play with the rules intentionally. His tremendous gifts allowed him to play with the rules all the more, thus allowing him to innovate.

 

[A Random User]

Ok... I can't help feeling I somehow just found myself on a forum discussing the
Da Vinci Code. Myself, I am not a believer of perfect anything in nature... I personally
believe this is all in what the observer, themselves, is wishing and wanting to see.
It is like finding faces in the clouds...

We as humans I believe try to seek out logic in a un-logical world in order to try and
come to terms with what we don't understand. The world can be a scary place and
only by trying to corral it and force it within a box, does it become tame...

With this said... I think it is crucial that we all try and stay on target, and respect others
views and comments, whether one agrees with them or not. The whole purpose of these
threads and the reason why I suggested them in the first place was to try show different
ways towards approaching designing bonsai. For some here, these ideas are going to be
something that clicks and they can relate, and will perhaps be able to put to use... for
others perhaps not.

However, if ideas are scoffed at or criticized , I think it then limits the amount of
ideas that are put forward. Cause I don't think too many people would be willing to throw out
any suggestions or ideas if they knew they were going to face an inquisition...

 

[A Random User]

So, as to better understand, can the subject please elaborate further how this works
as well as how one could possibly put these methods to work, since the goal here is
to help each other better our understanding of, as well as create better Bonsai.

What I am taking away from what has been put forth is that this is more of a scientific/mathematical
approach towards creating the perfect bonsai. Am I also correct in thinking that this approach
has the desired result of trying to create symmetry and harmony within the tree? If so, how
would it work with varying trees, as well as varying views of what is symmetric or harmonic?

This is not to try and argue against the use of this approach... quite the contrary. Instead
it is more to try and understand how this approach can work for all. If we all like and appreciate
different things, how can one establish the perfect tree if that perfect tree is
different for each of us ?

There needs to be a little bit more meat on the bones here. I think it would greatly help, if
this was laid out a little better and with more detail, so that everyone could come to terms with
what it is that is being suggested we all come to terms with.

 

[Smoke]

Let me see. My ancesters wrote the works.

Bonsai for thirty years, read about the sequence in Naka's books written in the 70's. Discussed it at length at the list server for Garden Web and later the forum, IBC, BonsaiPAGE, BonsaiTALK, BonsaiNUT, Bonsai Study Group, The Art of Bonsai and half a dozen books. I have read countless papers on the subject on the internet and have a book about the art.

In all that, what I have noticed is that the Divine Proportion, Golden Mean, Fibonacci Sequence is always mentioned in post production. For instance, in Gregs drawing of a formal upright tree, drawn at one third 33%, and the Golden Mean 38%. It is noticable, sure because they are 5% further apart. This is a 2 dimensional drawing trying to provide clarity for a three dimensional, living tree with a mind of its own and propensity to not grow branches exactly where Kepler tells us they should go.

so....since using a photo or a drawing or a painting where we can manipulate inanimate objects till our hearts content, could we maybe say the a tree looks better when it holds more true to the fundamentals of the Golden Mean? Could we say that maybe they are tools to help build a tree, but could never be used as a blueprint. One harsh winter or hot summer could blow a huge hole in Keplers masterplan in a hurry.

Happy bonsai shaping.

 

[coh]

OK____Who the heck designed the Fibonacci tree and what's the point of it? If it is a matter of poor choices, which is what this impossible tree presents, I would cut the thing down to the ground, start a fire and roast marshmallows. What are we supposed to be seeing and understanding. So far much of this is totally esoteric. If we are really being serious here someone pleas explain this one point with this one concept so that I can understand it.

I think that the "fibonacci tree" as drawn is a pretty poor example of the concept, and a much better explanation can be found at the link in the first post in this thread.

For me, what it boils down to is the following: in nature, there tend to be patterns that occur...examples often given are the spiral of a shell, the number of petals in a flower, the way the sunflower seeds are arranged. When these are analyzed mathematically, we often find the "golden ratio" is present. If you look at the fibonacci sequence of numbers...1, 2, 3, 5, 8, 13, 21, 34, etc - every number in the sequence is formed by adding the two previous numbers. Thus the next number after 34 would be 21+34 = 55. Now, if you start looking at ratios of these numbers you find some interesting things. Divide one number by its predecessor and you get the famous value 1.61 (55/34 = 1.61, 34/21 = 1.61, etc). If you take a particular fibonacci number and form the ratio of the first component to the total, you get .38. For example, for the number 34 (= 13+21), the ratio 13/34 = .38. For 21, the ratio 8/21 = .38, etc.

.38 of course is very close to .33 or 1/3, which relates to the bonsai "rule" about placing the first branch about 1/3 of the way up the trunk. And each succeeding branch would be placed roughly 1/3 of the remaining distance all the way to the top.

Similarly, in paintings one often places the "center of interest" near the 1/3 point in height and width.

These are of course not hard/fast rules that need to be applied in all cases, but it seems that humans are "wired" in some way to appreciate these kinds of ratios as being "beautiful". So we often tend to design things this way.

 

[Vance Wood]

Ok... I can't help feeling I somehow just found myself on a forum discussing the
Da Vinci Code. Myself, I am not a believer of perfect anything in nature... I personally
believe this is all in what the observer, themselves, is wishing and wanting to see.
It is like finding faces in the clouds...

We as humans I believe try to seek out logic in a un-logical world in order to try and
come to terms with what we don't understand. The world can be a scary place and
only by trying to corral it and force it within a box, does it become tame...

With this said... I think it is crucial that we all try and stay on target, and respect others
views and comments, whether one agrees with them or not. The whole purpose of these
threads and the reason why I suggested them in the first place was to try show different
ways towards approaching designing bonsai. For some here, these ideas are going to be
something that clicks and they can relate, and will perhaps be able to put to use... for
others perhaps not.

However, if ideas are scoffed at or criticized , I think it then limits the amount of
ideas that are put forward. Cause I don't think too many people would be willing to throw out
any suggestions or ideas if they knew they were going to face an inquisition...

I am only asking that if someone throws out an idea or concept that they are able to explain that idea or concept so that a dumb shit like me can understand it. Which still brings up another point: I still don't understand as yet how this applies to bonsai, unless it is a concept used to prove your work like some axiom in a geometry equation proof. So--in essence we are back to the rules and the adherence to them, assuming those who wrote the so called rules actually payed attention to all of the stuff we are talking about. For years we have been talking about how the so called rules should be ignored more or less unless our trees start looking like crap.

 

[Vance Wood]

I think that the "fibonacci tree" as drawn is a pretty poor example of the concept, and a much better explanation can be found at the link in the first post in this thread.

For me, what it boils down to is the following: in nature, there tend to be patterns that occur...examples often given are the spiral of a shell, the number of petals in a flower, the way the sunflower seeds are arranged. When these are analyzed mathematically, we often find the "golden ratio" is present. If you look at the fibonacci sequence of numbers...1, 2, 3, 5, 8, 13, 21, 34, etc - every number in the sequence is formed by adding the two previous numbers. Thus the next number after 34 would be 21+34 = 55. Now, if you start looking at ratios of these numbers you find some interesting things. Divide one number by its predecessor and you get the famous value 1.61 (55/34 = 1.61, 34/21 = 1.61, etc). If you take a particular fibonacci number and form the ratio of the first component to the total, you get .38. For example, for the number 34 (= 13+21), the ratio 13/34 = .38. For 21, the ratio 8/21 = .38, etc.

.38 of course is very close to .33 or 1/3, which relates to the bonsai "rule" about placing the first branch about 1/3 of the way up the trunk. And each succeeding branch would be placed roughly 1/3 of the remaining distance all the way to the top.

Similarly, in paintings one often places the "center of interest" near the 1/3 point in height and width.

These are of course not hard/fast rules that need to be applied in all cases, but it seems that humans are "wired" in some way to appreciate these kinds of ratios as being "beautiful". So we often tend to design things this way.

This would be fine if it was possible to get a tree to produce the branches you need at exactly the locations where you need them. Unless you are willing or able--- or willing and able to graft branches exactly where you need them, you're kind of stuck with who brought you to the dance and all of their faults.

 

[A Random User]

I am only asking that if someone throws out an idea or concept that they are able to explain that idea or concept so that a dumb shit like me can understand it. Which still brings up another point: I still don't understand as yet how this applies to bonsai, unless it is a concept used to prove your work like some axiom in a geometry equation proof.

I understand, and agree... I haven't had a chance to be able yet to put up any topics.
But will do soon... I don't have a problem if people don't agree with me, or ask me to
try and show how a theory could be able to put to practical use... I would just think this
should be what one should expect when putting forth ideas. I just think we need to understand
on both sides that one is not crazy for making a suggestion, and one is not crazy for asking
how this would work.

Myself, I have already put up my views regarding it. And I happen to agree with you.

 

[Bonsai Nut]

I am only asking that if someone throws out an idea or concept that they are able to explain that idea or concept so that a dumb shit like me can understand it. Which still brings up another point: I still don't understand as yet how this applies to bonsai, unless it is a concept used to prove your work like some axiom in a geometry equation proof.

Vance, I posted a link to it in my first thread. Here it is again.

Getting back to ground zero, the WHOLE reason I brought up this subject was in the spirit of a discussion around design. These patterns occur in nature, frequently, and humans see these patterns and are attracted to them. In my example I tried to illustrate how people would respond differently to two identical trees with slightly different primary branch heights. The one branch that satisfied or completed a natural sequence would look more pleasing.

My second point is that if you create a natural sequence, but skip a step (ie leave a void in the design) the eye will perceive balance even though a step is missing. Your subliminal mind will "see" a branch that isn't there.

This is not a literal discussion of "rules", but rather a way to think about tree design. It is a type of natural symmetry.

 

[A Random User]

Vance, I posted a link to it in my first thread. Here it is again.

Getting back to ground zero, the WHOLE reason I brought up this subject was in the spirit of a discussion around design. These patterns occur in nature, frequently, and humans see these patterns and are attracted to them. In my example I tried to illustrate how people would respond differently to two identical trees with slightly different primary branch heights. The one branch that satisfied or completed a natural sequence would look more pleasing.

My second point is that if you create a natural sequence, but skip a step (ie leave a void in the design) the eye will perceive balance even though a step is missing. Your subliminal mind will "see" a branch that isn't there.

This is not a literal discussion of "rules", but rather a way to think about tree design. It is a type of natural symmetry.

I think the response as well as the interest in these types of subjects is awesome !!! And I am
glad that you posted this. I have a very good feeling that this is going to be a nice way to spend
the winter, and come spring when a lot of folks start to break out those trees, they are going to
have a lot to digest !!!