The sea in your terminal

JavaScript (ES6) + HTML, 151 143 + 10 = 161 153 bytes

a=[48,15,57347,6147,1542,504];setInterval("a=a.map(n=>{for(x=-1;++x<80;)s+=' *'[n>>x%16&1];s+=`\n`;return n>>>15|n<<1},s='');O.innerHTML=s",99)

<pre id=O>

MATL, 41 40 bytes

`'3SJp/B@Tc`@+ara'F'* 'Za6el&Xx80:@-Z)DT

Example run:

Or try it at MATL Online! (the actual speed may depend on server load).

How it works

`                    % Do...while
  '3SJp/B@Tc`@+ara'  %   Compressed string (actually it's just a change of base)
  F                  %   Push false. Indicates base-95 input alphabet for decompression
  '* '               %   Push this string, which defines output alphabet
  Za                 %   Base conversion. This decompresses the string
  6e                 %   Reshape as a 6-row char array. This gives the basic pattern
  l&Xx               %   Pause 0.1 seconds and clear screen
  80:                %   Push array [1 2 ... 80] 
  @-                 %   Subtract iteration index to each element of that array. This
                     %    will produce the rotation via modular indexing
  Z)                 %   Use as column index. Indexing is modular, so this repeats
                     %   (and rotates) the pattern
  D                  %   Display
  T                  %   True. Loop condition for infinite loop
                     % Implicit end

HTML + CSS, 70 + 181 175 = 245 bytes

Makes use of text-shadow, rtl text and CSS keyframe animations.

a{display:flex;overflow:hidden;width:80ch}pre{text-shadow:16ch 0,32ch 0,48ch 0,64ch 0,80ch 0;direction:rtl;animation:w steps(16)1.6s infinite}@keyframes w{0%{margin-left:-16ch

<a><pre>**
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