4 grammar correction

Hi,

Coming from a specific field in algebraic geometry I am a total noob in Fractal Theory and I'd like to learn it a bit. I hope I am tolerated for my maybe-trivial questions. I just read about the Weierstrass-Mandelbrot fractal (it's also simply called Weierstrass fractal using the Weierstrass function.. but there are dozens of Weierstrass functions so I'd rather call it "Weierstrass-Mandelbrot" function). The definition of this fractal is easily found in wikipedia. I got easily impressed by it.

My question is whether there are nowhere differentiable continuous functions (between real numbers) that whose graph are not fractals? Is the WM function the easiest example of a nowhere differentialbe continuous function?

The other question is quite basic (for experts probably). I have seen the definition of fractal in wikipedia. This definition uses self-similarity. But in a reference of mine (from a lecture note) I get a definition that makes use of an inequality with Hausdorff-dimension and inductive dimension. Are these definitions equivalent or are the precise definition still under debate (my reference suggests that the suggested definition was former definition by Mandelbrot and then this definition was changed as Mandelbrot fractals don't follow this definition). A little enlightening would help :)

3 fixed spelling of Weierstrass

# Fractal questions: WeierstrauWeierstraß-Mandelbrot

Hi,

Coming from a specific field in algebraic geometry I am a total noob in Fractal Theory and I'd like to learn it a bit. I hope I am tolerated for my maybe-trivial questions. I just read about the Weierstrauss-Mandelbrot Weierstrass-Mandelbrot fractal (it's also simply called weierstrauss Weierstrass fractal using the weierstrauss Weierstrass function.. but there are dozens of weierstrauss Weierstrass functions so I'd rather call it "Weierstrauss-Mandelbrot" Weierstrass-Mandelbrot" function). The definition of this fractal is easily found in wikipedia. I got easily impressed by it.

My question is whether there are nowhere differentiable continuous functions (between real numbers) that are not fractals? Is the WM function the easiest example of a nowhere differentialbe continuous function?

The other question is quite basic (for experts probably). I have seen the definition of fractal in wikipedia. This definition uses self-similarity. But in a reference of mine (from a lecture note) I get a definition that makes use of an inequality with Hausdorff-dimension and inductive dimension. Are these definitions equivalent or are the precise definition still under debate (my reference suggests that the suggested definition was former definition by Mandelbrot and then this definition was changed as Mandelbrot fractals don't follow this definition). A little enlightening would help :)

2 added 3 characters in body; edited title

# Fractal questions: WeirstrauWeierstrauß-Mandelbrot

Hi,

Coming from a specific field in algebraic geometry I am a total noob in Fractal Theory and I'd like to learn it a bit. I hope I am tolerated for my maybe-trivial questions. I just read about the Weirstrauss-Mandelbrot Weierstrauss-Mandelbrot fractal (it's also simply called weirstrauss weierstrauss fractal using the weierstrauss function.. but there are dozens of weierstrauss functions so I'd rather call it "Weirstrauss-Mandelbrot" Weierstrauss-Mandelbrot" function). The definition of this fractal is easily found in wikipedia. I got easily impressed by it.

My question is whether there are nowhere differentiable continuous functions (between real numbers) that are not fractals? Is the WM function the easiest example of a nowhere differentialbe continuous function?

The other question is quite basic (for experts probably). I have seen the definition of fractal in wikipedia. This definition uses self-similarity. But in a reference of mine (from a lecture note) I get a definition that makes use of an inequality with Hausdorff-dimension and inductive dimension. Are these definitions equivalent or are the precise definition still under debate (my reference suggests that the suggested definition was former definition by Mandelbrot and then this definition was changed as Mandelbrot fractals don't follow this definition). A little enlightening would help :)

1