Golden Ratio Dragon Fractal (figured it out)

Click For Summary
SUMMARY

The Golden Ratio Dragon Fractal was successfully generated using MS Excel, although the user faced limitations due to Excel's precision and performance. The fractal was iterated 18 times before the program crashed multiple times, indicating that higher iterations may not be feasible on the user's hardware. The discussion raises questions about the necessity of the Golden Ratio in fractal generation and the potential effects of using alternative ratios such as 1.5 or 2.

PREREQUISITES
  • Understanding of fractal geometry concepts
  • Familiarity with MS Excel for mathematical modeling
  • Basic knowledge of the Golden Ratio and its applications
  • Awareness of computational limitations in software
NEXT STEPS
  • Explore advanced fractal generation techniques using Python libraries like Matplotlib
  • Research the implications of using different ratios in fractal design
  • Learn about optimizing performance in Excel for complex calculations
  • Investigate alternative software tools for fractal generation, such as Mandelbulb 3D
USEFUL FOR

Mathematicians, artists, and hobbyists interested in fractal generation, as well as Excel users looking to push the limits of the software for complex mathematical visualizations.

EebamXela
Messages
16
Reaction score
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
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?
 

Similar threads

Undergrad Dragon Curve Fractal Using Golden Ratio
  • · Replies 5 ·
Replies
5
Views
10K
High School Golden Ratio in Collatz-like sequences
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Arbirtary Extraction of Primes - From Ideal Fractal(s)?
  • · Replies 7 ·
Replies
7
Views
1K
Graduate Golden ratio fractal phase conjugation
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Fibonacci Series and Golden Ratio Explained
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Physically relevant: fractals, phi?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Fractals in relatively prime integers
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Is the Near Integer Muon to Electron Mass Ratio a Coincidence or Significant?
  • · Replies 7 ·
Replies
7
Views
4K
Hillbilly Fractal Antenna Reflector (and digital TV antenna suggestions)
  • · Replies 17 ·
Replies
17
Views
8K
Should Excel macros self-adjust when you delete lines above the affected cells?
  • · Replies 27 ·
Replies
27
Views
4K