Design: The Divine Proportion and natural sequences

[Bonsai Nut]

For an excellent background discussion... consider the Divine Proportion as it applies to bonsai. There are mathematical sequences that occur in nature that we are so accustomed to that we don't even know that we are seeing them... however their absence instantly makes something feel artificial. Because nature follows these sequences automatically, even in the occasion where a piece or part is missing (a broken branch, or a missing trunk) the balance of the design follows these "rules" so that the balance of the design feels genuine. There have been many excellent bonsai where I have commented on their use of "void space" - where you "feel" the bonsai that isn't there.

Rose petals follow the divine proportion... as do snowflakes... or pinecones.

 

[Bonsai Nut]

I think I may have lost some people on my last note So let me illustrate. Below are two trees. They each follow a different design "rule" or "guideline".

Which looks the most "natural" to you?

 

[berobinson82]

I think I may have lost some people on my last note So let me illustrate. Below are two trees. They each follow a different design "rule" or "guideline".

Which looks the most "natural" to you?

They look pretty identical.

 

[Jester217300]

Bottom branch is lower on the right pic.

I think the left pic feels more natural.

 

[qwade]

fibonacci #

I have always been fascinated by fibonacci numbers in nature. I try to find the sequence in all types of plants. Amazing enough they are there.Some are well documented. A google search would probably provide such examples. I have not used this in designing of my bonsai. Nor have I thought of this relation when viewing others' trees. Very interesting viewpoint made in the original post. Now I will be looking for those missing pieces as well as the visible ones when viewing bonsai. thanks

Indeed the left tree shows a fibonacci pattern.

 

[Bonsai Nut]

The trees are identical except for the height of the lowest branch.

The tree on the right uses the standard "rule" of bonsai of locating the first branch 1/3rd of the way up the trunk.

The tree on the left uses Divine Proportion to locate the branch where it would fit a natural sequence - i.e. 38% of the way up the trunk.

5% difference, but to me, it is noticeable.

I am not trying to say "from now on place all lowest branches 38% up the trunk". Rather I am trying to demonstrate the subliminal impact of natural order on design. We are surrounded by natural sequencing. When we create our bonsai, we should acknowledge this fact in our designs. It is a "natural element" of this art that is lacking from most other art forms.

 

[qwade]

I am not trying to say "from now on place all lowest branches 38% up the trunk". Rather I am trying to demonstrate the subliminal impact of natural order on design. .

I found it interesting that jester found the left tree more natural. Proves your point.

Gives me a whole new perspective in designing my trees. Ramification, internodes, branch placement takes on a whole new task when incorporating the divine sequence. Thanks again for this insight.

 

[tmpgh]

I am not a dummy. I mean it. I just... need help with visualizing the Divine proportion. I've read it over a few times. It says that you have to bisect the line segment in such a way that the smaller segment is the same ratio of the larger segment as the larger segment is of the whole line. I THINK I understand that theory, but I just cannot seem to wrap my head around it concretely. Can someone give me an example which includes visual and measurements?

I also like this sort of discussion here very much. Thanks guys!

 

[Bonsai Nut]

Taking it one step further, here's another tree:



Does this tree look "natural" to you, or not? (ignore my poor nebari attempt if you find it to distracting) Do you "feel" the lowest branch... on the right? The invisible one you can't see?

 

[Alain]

It is a "natural element" of this art that is lacking from most other art forms.

Actually I respectfully disagree.
Jackson Pollock painting were shown to be fractal even if he painted them before the discovery of fractal dimension in mathematics.
I'm myself an abstract painter and it's obvious that if a painting is fine it's because the different wavelengths of the colors used are in harmony (mathematical sense of the word), the disposition fit the right angles (for example the angles that a rocks will follow when it breaks), the symmetry or asymmetry rules are respected, and so on and so forth...
Of course when I paint I don't think about that, i just paint, like when a tree grows he doesn't really think about it, he just grows...

This is true for any kind of Art: I'm pretty sure Mozart didn't conscientiously know anything in mathematics, but his music proves us that he might have...

 

[Bonsai Nut]

This is true for any kind of Art: I'm pretty sure Mozart didn't conscientiously know anything in mathematics, but his music proves us that he might have...

He didn't know it. He "felt" it. Maybe we are agreeing on the same thing. I misspoke when I said it was "absent" from other art forms. I was thinking of it in a slightly different perspective.

 

[Bonsai Nut]

Can someone give me an example which includes visual and measurements?

Did you click on the link in my first post? Careful... it is a little bit of a rabbit hole. Read that article you'll start seeing sequences everywhere.

 

[qwade]

one aspect

I THINK I understand that theory, but I just cannot seem to wrap my head around it concretely. Can someone give me an example which includes visual and measurements?
!

 

[qwade]

Careful... it is a little bit of a rabbit hole.

This thread is a bit of a rabbit hole

 

[Bonsai Nut]

This thread is a bit of a rabbit hole

Kinda like the scene in The Matrix. Do you want the blue pill? Or the red pill? Reference to the rabbit hole is an expression based on Alice's Adventures in Wonderland. Once you go through you can't go back.

 

[Vance Wood]

Actually I respectfully disagree.
Jackson Pollock painting were shown to be fractal even if he painted them before the discovery of fractal dimension in mathematics.
I'm myself an abstract painter and it's obvious that if a painting is fine it's because the different wavelengths of the colors used are in harmony (mathematical sense of the word), the disposition fit the right angles (for example the angles that a rocks will follow when it breaks), the symmetry or asymmetry rules are respected, and so on and so forth...
Of course when I paint I don't think about that, i just paint, like when a tree grows he doesn't really think about it, he just grows...

This is true for any kind of Art: I'm pretty sure Mozart didn't conscientiously know anything in mathematics, but his music proves us that he might have...

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.

 

[Vance Wood]

This thread is a bit of a rabbit hole

Yes and sometimes you find a snake in the bottom of the hole looking for a meal. The only problem I am having with this post so far is a total lack of explanation. It is one thing to talk about the Fibonacci sequence but cannot or do-not describe what it is, the same with the golden mean etc.

 

[qwade]

The only problem I am having with this post so far is a total lack of explanation. It is one thing to talk about the Fibonacci sequence but cannot or do-not describe what it is, the same with the golden mean etc.

I thought the link in the original post explained the ratio----- but in simple terms the fibonacci sequence is a sequence of----- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Add any 2 consecutive numbers in order and the sum will be next number in the sequence. ex. 13+21=34. The golden ratio in simple terms is the ratio between these numbers. Again using the sequence divide any 2 numbers in sequence and you will approximate the ratio. ex. 34/21=1.619 . The ratio gets more accurate as you move up in the fibonacci sequence. It is notated by the greek letter phi. and usually expressed as 1.618.

I hope that helps you Vance.

 

[Alain]

Maybe we are agreeing on the same thing.

I'm sure we do!

What I meant is: any piece of Art has to follow the Natural laws otherwise it's just not right.
An artist is just in harmony with these laws, even when he doesn't 'know' them, which explain why his work follows them, and also why all kids are artists...

 

[Vance Wood]

I thought the link in the original post explained the ratio----- but in simple terms the fibonacci sequence is a sequence of----- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Add any 2 consecutive numbers in order and the sum will be next number in the sequence. ex. 13+21=34. The golden ratio in simple terms is the ratio between these numbers. Again using the sequence divide any 2 numbers in sequence and you will approximate the ratio. ex. 34/21=1.619 . The ratio gets more accurate as you move up in the fibonacci sequence. It is notated by the greek letter phi. and usually expressed as 1.618.

I hope that helps you Vance.

I guess it is up to me to ask questions where others are afraid they will be accused of being challenged? How do these things apply to bonsai?