Attributes specified in the class declaration are called class attributes. Consider the following example:

class Newton:
    tol = 1e-8 # this is a class attribute
    def __init__(self,f):
        self.f = f # this is not a class attribute
    ....

Class attributes are useful for simulating default values and can be used if values have to be reset:

N1 = Newton(f)
N2 = Newton(g)

Both instances have an attribute, tol, with the value initialized in the class definition:

N1.tol # 1e-8
N2.tol # 1e-8

Altering the class attribute automatically affects all the corresponding attributes of all instances:

Newton.tol = 1e-10
N1.tol # 1e-10
N2.tol # 1e-10

Altering tol for one instance does not affect the other instance:

N2.tol = 1.e-4
N1.tol  # still 1.e-10

But now N2.tol is detached from the class attribute. Changing Newton.tol no longer has any effect on N2.tol:

Newton.tol = 1e-5 # now all instances of the Newton classes have 1e-5
N1.tol # 1...