The question leaves a lot of room for interpretation:
- First digitally made image for a screen (tv or cinema) vs first ever digitally created image that was not publicly broadcast?
- Or - first photorealistic CG for screen (which means you cannot tell it is not real)?
- First moving image? Or still image?
- First in commercial production (e.g. Hollywood film)? Or any type of animation or effect, regardless of the market and final destination?
- 2-dimensional or 3-dimensional? (or 2d or 3d?)
- And finally: hardly ANY image ever is created by "computer algorithm". Human hand has quite an input, unless we are talking random number generators which influence some fractals and particles perhaps... So, all of these were created by actual programmers and artists, and algorithms were mere help in the process, usually for rendering. Models, animations, textures, and so on are all done by hand, albeit, on the computer. Even things such as motion capture (or performance capture) have heavy input from an animator.
The first character animation that was ever made on a computer was actually done in Russia as an analysis of cat walk cycle around 1968. It was done on a computer, then output on hundreds of sheets of paper and shot on film. This was not photo-realistic, but motion was excellent.
The first animation done on a computer, that was not character was done in Sweden, and broadcast on TV in 1961. I believe it was black and white, lines (vector graphics), simulation of a highway.
The first use of 3D was in Futureworld, but it was created earlier at University of Utah. Soon after we saw the death star animation in Star Wars (a year later).
Westworld had the first 2D effect, raster graphics, a few years earlier 1974 I think. Not nearly as complex to do as 3D and it was computer processed (not entirely computer generated as it used filmed footage as a starting point).
The first use of photorealistic effects created on a computer, depending on how we define "photo-real" was probably original TRON (1984). Most of the effects work was actually in-camera work (with UV lights and such), but those light-bikes were CG entirely.
First ever fully animated photo-real 3D character on TV screen was Young Sherlock Holmes in 1985. Soon followed by series of excellent TV commercials done by the same studio (Robert Abel and Associates) for Benson & Hedges.
The first use of 2D photo-realistic effect was in Willow (1988). That was also the first use of morphing effect.
The first use of fully photo-realistic 3D effect which included the hardest thing to do - humans faces blended with bodies and environment - was "Death Becomes Her". This was the true revolution in Computer Graphics and VFX.
And then there are more firsts that come to mind:
The first fully animated 3D short in full color, using squash and stretch, motion blur, plenty of procedural models and all other things that make it truly entertaining was probably "Andre and Wally B" by ILM/Pixar.
The first fully animated 3D short with all the great qualities of good animation that also won an Oscar was Tin Toy by Pixar (1988). This short inspired the film Toy Story which came out much later (illustrating well how long it can take to take an idea from script to screen when you are creating everything using computers).
The first music video using 3D animation was "Hard Woman " by Mick Jagger
The first fully 3D animated music video was "Money For Nothing" by Dire Straights (also the first production that I know of that had to be done twice as all their data was lost toward the end of the production).
The first TV commercial that was fully 3D was "sexy robot" inspired by Hajime Sorayama, for canned foods (available on youtube). You can also see the making of there.
The first fully animated 3D CG feature length film was "Toy Story" - 1996.
The first 3D morph that still looks stunning was "Black or White" music video by Michael Jackson, effect created by PDI (today known as Dreamworks, unfortunately, N. Cal office which was PDI was closed recently)
The first use of CG water and liquid effects was Terminator 2 done by ILM.
The first use of photo-realistic, fully integrated 3D CG characters with live plate was probably Jurassic Park, courtesy of the same person who did T-2 - Spaz Williams.
There are other firsts, like the work that was not as well known but certainly important for this industry, like the work of Evans and Sutherland who pioneered interactive 3D CG, and all the good stuff that was going on at NYIT and University of Utah.