If President Reagan achieves nothing else in his campaign to cut federal regulations, he will at least go down in history as the president who deregulated Mud Creek.

Mud Creek is an aptly named stream (average depth, 6 inches) that trickles through a cornfield just outside Appleton's city limits. Last year, a group of downtown business leaders tried to win federal protection for the creek under environmental laws governing navigable waterways. The action was taken not to protect Mud Creek's ecology, but rather to create a legal obstacle that would block construction of a big new shopping mall planned on the site of the creek--a mall that presumably would drain business from downtown Appleton.

A year ago, the city leaders thought they had a good chance to win U.S. protection for the creek. Today, that hope is gone. The Army Corps of Engineers has formally declared that Mud Creek does not meet the legal standard for protection. Reagan rescinded an executive order issued by his predecessor that directed federal agencies to help downtown areas facing suburban commercial threats like the one downtown Appleton fears.

Despite all that, Mud Creek is still in place, and the mall is going nowhere. The mall's developers, having fought nearly a year to stave off federal intervention, now face a brand new battle from a brand new set of regulators--the state of Wisconsin.

The downtown merchants have dusted off a whole series of state laws and regulations that would, they claim, prohibit construction of the new mall. The Battle of Mud Creek will probably be fought in the courts for years to come.