Shares of online real estate service Zillow more than doubled in their initial public offering on Wednesday, following the same path as other prominent Internet companies that have recently gone public. Zillow priced its offering at $20 per share on Tuesday night, but demand pushed shares up to $57 upon opening on Wednesday. Shares briefly soared above $60 before settling back to around $38 per share in midday trading. Zillow’s initial public offering follows filings by a slew high-profile Internet companies such as Groupon, LinkedIn, and Zynga. Some of these companies have continued to…