Golden Ratio Dragon Fractal (figured it out)

In summary, the conversation discusses a fractal that the speaker had trouble creating in November, but has since figured out how to make using MS Excel. However, there are still some gaps in the fractal that are likely due to the program's limited precision. The speaker was only able to iterate the fractal 18 times and their laptop struggled with the final step, causing Excel to crash multiple times. They also mention a higher resolution image and pose a question about using different ratios for the fractal.
  • #1
EebamXela
16
0
Back in november I asked the forum about this fractal:
http://en.wikipedia.org/wiki/File:Phi_glito.png

At the time I couldn't figure out how to make it.

Since then I've figured it out. I used MS Excel.

pyUJR5e.gif


I'm not completely satisfied though. There are some gaps between the major portions of the fractal that I'm pretty sure are a result of the limited precision of Excel. I'm not so good with coding, so I just brute forced it with the only program i know well.

Also, I was only able to iterate the fractal 18 times. My laptop was struggling hard to iterate the final step and even failed several times to do so. Excel crashed like 4 times in the middle of calculating. So i think a 19th is out of the question given my limited abilities.

Hi resolution:
http://i.imgur.com/lKXzIBH.jpg
 
Mathematics news on Phys.org
  • #2
Is the Golden Ratio a requirement? If you were to use 1.7, or 1.6, or 1.5, or 2, how different would the figure be?
 

What is the Golden Ratio Dragon Fractal?

The Golden Ratio Dragon Fractal is a mathematical fractal that is created by repeatedly applying a simple algorithm to a starting shape, resulting in a complex and visually appealing pattern.

How is the Golden Ratio used in the fractal?

The Golden Ratio, also known as the divine proportion, is a mathematical ratio that is approximately equal to 1.618. In the Golden Ratio Dragon Fractal, this ratio is used to determine the proportions and angles of the shapes that make up the fractal, resulting in a visually pleasing and harmonious design.

What is the significance of the Golden Ratio in nature?

The Golden Ratio can be found in many natural phenomena, such as the spiral patterns of seashells, the branching patterns of trees, and even in the human body. This ratio is believed to create a sense of balance and beauty, and is often referred to as the "mathematical fingerprint of nature".

How is the Golden Ratio Dragon Fractal created?

The Golden Ratio Dragon Fractal is created by starting with a rectangle that has a width-to-height ratio of 1.618. This rectangle is then divided into smaller rectangles using the Golden Ratio, and the process is repeated on each smaller rectangle until a desired level of complexity is achieved.

What are the practical applications of the Golden Ratio Dragon Fractal?

While the Golden Ratio Dragon Fractal is primarily a mathematical curiosity, it has been used in various fields such as art, architecture, and design. Its visually pleasing and harmonious nature makes it a popular choice for creating appealing designs and patterns.

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