The PHANTOM GRAPHS

of Philip Lloyd (Aukland NZ)

TSM Resources

Blog

Phantom Graphs Blog
Intersecting Planes

The three phantoms of a quartic

y = x^n

The Strange Behaviour of y = x^n (.pdf)

y = x^x

The graph of y=x^x (.pdf)
The Spiral Equation (.agg)

y = (–1)^x

Discussion
Autograph file (.agg)

y = (–2)^x

Discussion
Autograph file (.agg)

y = (–b)^x

Autograph file (.agg)

3D visualization of y = (-1.25)^x

y^x = x^y

The Perplexing Problem of y^x=x^y
New Points on y^x=x^y

y = ln(x)

With Complex y-plane (.pdf)

x^6 = x^3

The solutions of x^6 = x^3
Autograph file (.agg)

From Flatland to the 4th Dim (.pdf)

Fundamental Theorem of Algebra (.pdf)

Mapping Phantom Graphs