Design: The Divine Proportion and natural sequences


Ahh the fake golden spiral ..... Not really a spiral but a series of arcs glued together.
 
Last edited by a moderator:
What was discovered down here was simply.

Grow one type of tree many times - say 30 efforts, study it, apply what you know to a seedling or cutting and you can draw an image of what you want, before you have a tree effort.

Drawing first an outline, and then branches, you can - Think With a Pencil - and create a tree from scratch.

Essentially seeds / cuttings can be treated as a blank canvas.

This image is still the best example of the technique.
[ to do many 3" or smaller Gmelina were grown before the prime effort was attempted.]

Traditionally trained Oil Painters, don't really compose images, with the Golden rule or other, they work with either abstract patterns of light and shadow or outlines or other.
It is instinctive, though at a later date, mathematical situations can be found.
See the - Secret Geometry in Paintings.

You have seen these images before, but this should get the point across.
Good Day
Anthony

* If you study the same tree type in nature, and DRAW the images, with time you can pick the best parts and instinctively, unconsciously, as in breathing, create the tree of your imagination.
 

Attachments

  • gmelina design.jpg
    gmelina design.jpg
    45.2 KB · Views: 31
  • gmelin10.jpg
    gmelin10.jpg
    69.7 KB · Views: 29
We all have trees we like and don't like.

I'm willing to bet the ones we like better, fit more into the sequence. (Go see for yourself)

Few times, if any, Will we actually design according to it directly, unless grafting.

Will you remove a healthy branch with foilage near the trunk because a crappy one grew 5% lower? No.
But you can adjust it, and everything else to better fit the sequence. And you should!

I agree with the clump tree being hard to figure.
But the stick pine is very noticeably different.

However, you ought not look to SEE. Rather, look to FEEL. and it is easily noticed.

Sorce
 
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.

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.

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.

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.

I think that the "fibonacci tree" as drawn is a pretty poor example of the concept

I agree with the clump tree being hard to figure.
But the stick pine is very noticeably different.

I'm sorry I ever posted the diagram of the tree. Totally changed the conversation. If I where thin skinned or sensitive I would feel I was being attacked on this forum.I was just trying to add to the conversation. I obviously failed miserably.
 
Last edited:
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.


Although I always try not to use a definitive statement in these situations------ Yes 'some' would have been a better choice than 'most'. I stand corrected
 
Yes it would be hard to design a tree with the exact proportions of the golden ratio. Some would find it interesting to try
 
Last edited:
I'm sorry I ever posted the diagram of the tree. Totally changed the conversation. If I where thin skinned or sensitive I would feel I was being attacked on this forum.I was just trying to add to the conversation. I obviously failed miserably.

Here we go-----I hope not. No one was attacking you, but if you post a picture of a tree that is supposed to be representative of the concepts you are trying to explain and the tree you post is unbelievably convoluted. It is difficult to impossible to decide what anomaly is on purpose and essential to the equation and what is just a bad diagram. You have to post things that people like me can understand. In conversations like this, details are crucial and if you (meaning the reader) cannot understand what is essential and or crucial, and instead dwell on the irrelevant, you have solved nothing. I guess you guys can't see the forest for the tree. Posting things like the previous post does not help one little bit. Roosteer Cogburn said it best: "No one likes being called low down and foul smelling."
 
Last edited:
I'm sorry I ever posted the diagram of the tree. Totally changed the conversation. If I where thin skinned or sensitive I would feel I was being attacked on this forum.I was just trying to add to the conversation. I obviously failed miserably.

I laughed out loud when I saw your tree. It made my day. But I understood your point - which was to display the growth of ramification as a Fibonacci sequence :) I actually hadn't thought of it that way before but you are absolutely right. There are many ways to design the "rate" of ramification. We have seen trees that have been overdone that look like puffballs, or trees that have been underdone, but a "perfectly" ramified tree (to the eye) will probably fit the sequence pretty closely. So at least ONE person benefited from your drawing :)

And as someone pointed out... if you wacked off half the tree, you would still be in sequence. The point being (and I truly believe this) that the human eye sees what it expects to see - which is NOT necessarily what is there. If you design to a natural sequence, even if the design is incomplete, the mind will fill in the missing blanks, and the tree will be balanced. If you BREAK the sequence in your design, it will either look unnatural, or will make a powerful design statement that the mind will seek to reconcile / understand. Most of the times this happens it is because people don't understand what they are doing and we think of it as "bad" design. But sometimes it is done purposefully, and it yields art that is unique and sublime.

I have often said... you need to understand the rules before you break them. It is the difference between design with a purpose, and blind luck. And by "understand the rules" I don't mean take a lot of bonsai classes or read a lot of bonsai books (necessarily). It may just mean "spend a lot of time looking at trees in nature". In this way you become familiar with natural sequences, and your design work will reflect this, even if you have never read a bonsai book in your life.
 
I don't understand any of this. Don't really see the need to try. I know a good looking tree from one that is not. That is all I really need. No need to worry about codes or spirals. Just trees.
 
Ahh the fake golden spiral ..... Not really a spiral but a series of arcs glued together.

It's a digital representation of an analog concept. Phi, like Pi, is a non-ending, non-repeating number. People use 1.68 for Phi just like they use 3.16 for Pi... but the reality is that it approaches a limit but never quite gets there. In fact, I would argue that you can draw the limit, but you can't ACTUALLY draw the reality - because you will never be accurate enough :) (insert weird math argument here)
 
So aside from the obvious "rule" about branches being located at the 1/3 points on the trunk, has anyone looked at how these ratios may be applied elsewhere in the tree? For example, when designing the branches, do trees tend to look "good" when the branch thickness is about 1/3 of the trunk thickness at that point? And what about ramification, should the first split of the branch be at the 1/3 point (of it's total length)?

The other thing that interests me, and this is very hard to quantify - there are trees that appear to break all the rules, are very asymmetrical, etc - yet often (to me, at least) these are the most attractive trees. So if one were to analyze these types of trees, would one find that the way the "rules" are broken somehow fits into the ratio? I don't know if I've expressed what I mean clearly enough here...
 
I don't understand any of this. Don't really see the need to try. I know a good looking tree from one that is not. That is all I really need. No need to worry about codes or spirals. Just trees.

I don't need to understand gravity to know that if I drop a bottle of beer it will fall to the ground (and probably break on my foot). How? Why? It is because I have become so used to the rules of nature that I take them into consideration without even thinking about it.

Had you never seen a tree in nature, I'll bet your bonsai would be poor. You have seen trees - lots of them - and your mind has become programmed to see natural sequences - even when you don't "know" that you are seeing them.
 
Actually Chris [ Coh ]

the rule of thumb given to us was ,

0.75 of the trunk - 1st branch
0.50 of the trunk - 2nd branch
0.25 of the trunk - 3rd branch
and after that you can eye it.

What was observed in photographs with the response of the viewer, the proportion is so natural that very few realised that trunk had any thickness, unless a tape measure was placed near the tree or some other recognizable object.

However, check and see how many exhibit trees with very thin branches, and how quickly it is observed that the trunk is thick.

Now here is the kicker, if you design a tree with a thick but well tapered trunk, and thin branches, imagine how much will change as the branches fatten, and how off the design goes.
Good Day
Anthony
 
The other thing that interests me, and this is very hard to quantify - there are trees that appear to break all the rules, are very asymmetrical, etc - yet often (to me, at least) these are the most attractive trees. So if one were to analyze these types of trees, would one find that the way the "rules" are broken somehow fits into the ratio? I don't know if I've expressed what I mean clearly enough here...

Well I guess the bottom line would be that beauty is in the eyes of the beholder. The ratio could just be a coincidental number that works well when applied to objects in nature. Going forward, for me at least, I would like to see how the ratio fits into Bonsai--- such things as the example you provide above. I've read a lot about this subject with other things in nature trees included, but until this thread have never applied it to Bonsai.
 
Well I guess the bottom line would be that beauty is in the eyes of the beholder. The ratio could just be a coincidental number that works well when applied to objects in nature. Going forward, for me at least, I would like to see how the ratio fits into Bonsai--- such things as the example you provide above.

Here you're wrong. People DON'T perceive "beauty" differently. These sequences have been used over and over in design - in art - in architecture - to create natural order/balance. The Parthenon. The Mona Lisa. Classic examples. If people can "wing it" and end up with a design "that works" it can be evaluated within the context of these sequences to understand it.

It is also interesting to note - they are present in different cultures / countries / peoples. They are used in Eastern art as well as Western art. Classic examples are Japanese formal garden design - rock gardens - pebble gardens, etc.

When you might use it in bonsai:

Taper of trunk
Taper of branches
Arrangement of branches
Placement of apex
Height of tree
Outline of silhouette
Rate of ramification
Placement of tree in pot
Display of pot on stand
Arrangement of formal bonsai display

I think the better question would be: when WOULDN'T you use it in bonsai. Because most of the classic sins on bonsai break natural sequencing:

No taper
Reverse taper
Double branches
Bar branches
Bad placement in pot
Pot too big, pot too small
Etc, etc...
 
Here you're wrong. People DON'T perceive "beauty" differently.

I don't think I could agree with that statement.

For example. We see beauty in an old contorted tree hanging on to life. Others see a dead tree with no such beauty.
 
I don't think I could agree with that statement.

For example. We see beauty in an old contorted tree hanging on to life. Others see a dead tree with no such beauty.

It may be that there are certain "factors" that we are wired to think are beautiful, and the golden ratio may be one of them. But, then you have to add on top of that your life experiences, what you are taught, the environment you grow up in, etc. So that would allow one person to see beauty in the old contorted tree while to another it is an eyesore. Or one person sees beauty in Picasso while others just see "WTF".

As for those old contorted trees, in my experience some are more beautiful than others. It would be interesting to determine if people tend to respond favorably to the same types of old contorted trees and if so, is there something quantifiable about them...golden ratio or something else. It doesn't mean that you get out the rulers and design all your bonsai that way, but perhaps it would given insights that would allow more people produce more effective trees. Maybe not but it is an interesting topic.

Chris
 
Back
Top Bottom