Interesting plot of an implicit equation with square root of signum functions

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SUMMARY

The discussion centers on the "Batman graph," an implicit equation that utilizes signum functions and involves the square root of negative numbers, which are undefined in real number space. The Python code provided successfully plots this equation despite the mathematical inconsistencies, as it discards complex numbers. The conversation highlights the importance of understanding variable ranges and the nature of curves in implicit equations, particularly noting that some curves do not represent functions in the traditional sense.

PREREQUISITES
  • Understanding of implicit equations and their graphical representations
  • Familiarity with signum functions and their properties
  • Basic knowledge of Python programming and plotting libraries
  • Concept of complex numbers and their implications in graphing
NEXT STEPS
  • Explore Python libraries for plotting implicit equations, such as Matplotlib
  • Study the properties and applications of signum functions in mathematics
  • Learn about the implications of complex numbers in graphical representations
  • Investigate the differences between functions and curves in mathematical contexts
USEFUL FOR

Mathematicians, data scientists, and Python developers interested in visualizing complex mathematical concepts and exploring the nuances of implicit equations.

Micko
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Hello,

recently, I have found so called Batman graph and equation, which basically plots Batman sign.

I have even found Python code that plots this implicit equation.
Code can be found here:
.

And the equation is given here:
[url]http://i.imgur.com/CNy9J.jpg

If you look closelx, you'll see that there are a lot of signum functions and for many numbers that belongs to the graph, there is square root of negative number which is not defined in real number space.
This is a warning sign that equation is not good.
But somehow, if you use this equation it still plots OK.

I cannot explained this. Can you help me understand this?

Python plot just discard nonsence and doesn't plot (naturally) complex numbers.
 
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It's probably easy to explain if we saw the equations. Firstly the range of the variables have to be taken into account and secondly, some curves are no functions, so it looks as if e.g. ##y^2=x## is used instead of ##y=\sqrt{x}## which would be only one branch.
 

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