The PHANTOM GRAPHSof Philip Lloyd (Aukland NZ) 


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The three phantoms of a quartic 

Cubic phantoms Quartic phantoms 
Autograph file (.agg) Autograph file (.agg) 

y = x^n 

y = x^x 
The graph of y=x^x (.pdf) 

y = (–1)^x 
Discussion 

y = (–2)^x 
Discussion 

y = (–b)^x 
Autograph file (.agg) 
3D visualization of y = (1.25)^x 

y^x = x^y 

y = ln(x) 
With Complex yplane (.pdf) 

x^6 = x^3 


From Flatland to the 4th Dim (.pdf) 











