The Tachyon plugin is responsible for replacing WordPress' default thumbnail handling with dynamic Tachyon URLs.

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Install the Tachyon plugin as a regular plugin in your WordPress install (mu-plugins also supported).

You also need to point the plugin to your Tachyon server. Add the following to your wp-config-local.php:

define( 'TACHYON_URL', 'http://localhost:8080/<bucket name>/uploads' );

The Tachyon plugin is based on the Photon plugin code by Automattic, part of Jetpack. Used under the GPL.