Some cryptocurrencies do not provide a way of mining their native asset. EOS is one of those projects, although it seems  a PoW-oriented clone has surfaced recently. 

People who have an interest in EOS will not be able to mine the currency.

EOSPoW Utilizes EOS to Mine Coins

That is a deliberate choice made by its developers.

For reasons unknown, some developers feel that situation is not right.

As such, a Proof of Work version of EOS called EOSPoW, exists today. 

It utilizes the mining algorithm and difficulty adjustments of Bitcoin, as well as a very similar emission system.

There will be 21 million POW minted in total., which is expected to take several years.

Interestingly enough, this new project utilizes some core aspects of the normal EOS.

The CPU and NET resources offered by EOS will be used to mine POW by moving EOS to Eosiopowcoin.

Every time the contract receives an EOS transfer, that amount of funds, as well as 0.0025% of the POW supply in the account is distributed to users.

A very interesting approach to creating a new currency, although it remains to be seen if it has a chance of success.

This is not an airdrop or forked currency, thus no free coins are distributed to existing EOS holders.