You don't necessarily need DLNA for that, nor HDMI. WiFi and the right app might do as well. Take a look at e.g. Remote Gallery 3D, you cannot only have a slide show on your PC, but even manage your photos remotely. The app runs a web server on your device, which then can be accessed via any web browser (i.e. completely OS independent). Only requirement is Flash capability. For a presentation, also have a look at Youtube.
This way you can even take your photo gallery with you when visiting friends or family: no installation on the PC required. So as long as WiFi is available, you're fine. The app is free, so it comes without investing any extra money, as requested ;)
Alternatively, you could setup a DLNA server on your Android device (BubbleUPnP would be a good choice for that). Nex, you would need a client to access it from your Mac (take a look at this Wikipedia list to pick one). Start the server on your Android device, then start the client on the Mac. The Client should automatically find and list your Android device, and let you browse your media. What features are offered (just pick single entries, make a slideshow, have background music played along) depends on the client chosen.
A third variant would be investigating in Airplay. As that's Apple's own stuff, your Mac should surely support it. There are a bunch or apps supporting Airplay you could chose from; not having a Mac, I cannot be of assistance in this area.
Fazit by ILIV:
BUbbleUPnP is a very nice software. I'm having a lot of fun trying out various combinations. One thing I learned this morning is that I can use VLC to browse and play all content on my phone: video, music and pictures. Video playback intermittently stucks for a split second, very rarely, but it does. That is unfortunate, but I'm wondering if it is a VLC or BubbleUPnP issue, or maybe it's just that two don't get along well.