Forex.com is one option, not a brilliant one but they do allow 0.01 lots and have no maximum lot limit.
It really depends what your starting lot size is going to be.
To be honest I would not use any broker that is not an ECN or an STP, especially not for a martingale. Get a requote or some other kind of order rejection at the wrong time and you are in the deep stuff.
One of the reasons Martingales are such a dicey proposition on live accounts.
11:15, restate my assumptions: 1. Mathematics is the language of nature. 2. Everything around us can be represented and understood through numbers. 3. If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature.