To get arbitrary exponents I rely on two identities
z = r e ^ t = r(cos t + i sin t)
and
a^b = e^(b ln a)
then
z0 = a + bi
r0 = | z0 |
t0 = atan(b/a)
r1 = e ^ (exponent * ln( r0 ) )
t1 = t0 * exponent
z1 = r1( cos(t1) + i sin(t1) ) + c
z = r e ^ t = r(cos t + i sin t)
and
a^b = e^(b ln a)
then
z0 = a + bi
r0 = | z0 |
t0 = atan(b/a)
r1 = e ^ (exponent * ln( r0 ) )
t1 = t0 * exponent
z1 = r1( cos(t1) + i sin(t1) ) + c
Comments
I imagine all of this will work on the Julia set, as well.
Nicely done.