Stromatolites are bacterial mats and colonies forming identifiable patterns. In Earth they have existed 3.5 billion years. You can read more about them in articles Wikipedia: Stromatolite and J. William Schopf 2007: Evidence of Archean life: Stromatolites and microfossils
Note in the articles the patterns that stromatolites form in Earth and compare them to images below. The following science publications by Rizzo, Bianciardi, Farias and Cantasano are also worth to read:
Vincenzo Rizzo, Nicola Cantasano, International Journal of Astrobiology, September 2016:
Structural parallels between terrestrial microbialites and Martian sediments: are all cases of ‘Pareidolia’?
Vincenzo Rizzo,Maria Eugenia Farias, Nicola Cantasano, Daniela Billi, Manuel Contreras, Francesca Pontenani, Giorgio Bianciardi, Cell Biology 2015: Structures/textures of living/fossil microbialites and their implications in biogenicity. An astrobiological point of view
Giorgio Bianciardi, Vincenzo Rizzo, Maria Eugenia Farias and Nicola Cantasano, Astrobiology Outreach 2015: Microbialites at Gusev Crater, Mars.
Vincenzo Rizzo and Nicola Cantasano 2009, International Journal of Astrobiology 8(4), Possible organosedimentary structures on Mars
V.Rizzo and N.Cantasano 2011, Mem. S.A.It.Vol.82, 2011, Textures on Mars: evidences of a biogenic environment.
V,Rizzo,International Journal of Astrobiology, Cambridge University press, March 2020: Why should geological criteria used on Earth not be valid also for Mars? Evidence of possible microbialites and algae in extinct Martian lakes
The method by Rizzo, Bianciardi and Cantasano has been mathematical comparative analysis of images of Earth microbialities and corresponding Martian candidate microbialities, indicating that Martian microbialities are biological with 99.6% probability. Here is direct quote of this conclusion chapter of 2011 article:
The inorganic sedimentary processes follow simple rules, whereas the structures we described denote complex products, congruent to the terrestrial biogenic environment: life has existed and is still alive on Mars.
Below is few images with possible stromatolite patterns and formations in Mars by Curiosity and Opportunity.
The Curiosity Sol 632 image has repeating hexagonal patterns.Similar patterns are visible also in Pilbara region, Australia, as a result from microbial activity. NASA has established a research co-operation with Australian Macquarie University to compare the Pilbara region microbial fossil formations with similar Mars formations. See web-site by Dr.Simon George and Dr.Carol Oliver: NASA Macquarie University Pilbara Education Project . The Pilbara region has 3.43 billion year old microbial reef. The Sol 632 observation was done by Dr.Lyall Winston Small. See also Dr.Small's book about Martian stromatolites: The Living Rocks of Mars (2015).
Good investigation about this subject is by Nora Noffke, Astrobiology Volume 15, Number 2, 2015:
Similar excellent investigation is Giorgio Bianciardi, Vincenzo Rizzo, Nicola Cantasano, 2014: Opportunity Rover’s image analysis: Microbialites on Mars? .
A good site about ancient microbial Earth fossils is by Ph.D. Ian West: Fossil Forest, Lulworth Cove; Part 1: The Ledge and Strata, Geology of the Wessex Coast of Southern England . The similarities between Earth stromatolites and corresponding Mars objects is striking. I have had discussions with Dr. West. He supports the view that the objects presented in this article as candidates for stromatolites and thrombolites in Mars is correct. When Dr. Small wrote the first version of his book The Living Rocks of Mars , Dr. West kindly gave his valuable feedback to Dr.Small via Harry.
Sol 528 stromatolite or thrombolite ? Dr. Ian West has pointed out of Sol 528 object that both the Purbeck thrombolite (on Earth, England) and the Sol 528 thrombolite candidate have radial cracks, which may be result of burial. And if so, then the Martian examples may have been buried and re-excavated by erosional processes. The Purbeck thrombolite image is by Dr.West. Dr.Lyall Winston Small has interesting idea about Opportunity Sol-251 object named Wopmay in [136]: Could stromatolites be living on Mars even today? Note that there is also Blueberries on this object. The name Wopmay relates to history of stromatolite research on Earth. Could Sol 1257 contain microbial mats growing today? Sol 731 thrombolite?
On 9th of March 2016, Sol 1276, Curiosity arrived to a place which seems to have a lot of objects resembling stromatolites. Curiosity stopped to investigate them and it took large number of images with MAHLI and ChemCam. On Sol 1433 there is similar object.
Below are images by Opportunity microscopic imager. Things to consider here are stromatolites, bacterial mats, layers cemented by microbial slime. I recommend visiting the web-site by Canadian scientist Michael Davidson about these: Mars Fossils, Pseudofossils, and Problematica . He made the analysis year 2004 when Spirit and Opportunity had been only few months in Mars. In images A, B, C and D besides the possible stromatolites, the empty voids also have interesting patterns. The 'Martian Rotini' feature in image E caused much debate about possible fossils in Mars.
See also site about Earth stromatolites by Richard Thieltges: Evolutionary research - Stromatolite Identification Site . Thieltges has the largest collection of Stromatolite fossils in North America. NASA has borrowed his collection to educate the Mars rover scientists. And read: S. Leuko, L. J. Rothschild, B. P. Burns, Halophilic Archaea and the Search for Extinct and Extant Life on Mars and Mark Strauss October 17, 2016: NASA’s Bold Plan to Hunt for Fossils on Mars .
Interesting article is in Universe Today, November 2019 Evan Gough Scientists Search for Ancient Fossils in Australia, Practicing the Techniques They’ll Use on Mars . NASA and ESA scientists are practicing the identification of stromatolite and microbialities fossils on Mars for coming Mars 2020 and ExoMars rovers. The practicing area is in Pilbara Australia, where are well preserved Earth stromatolite fossils. Well done Ken Farley, Mitch Schulte and Martin Van Kranendonk. But it is sad that the work of pioneers, Rizzo, Bianciardi, Cantasano, Noffke and several citizen scientists(Small, Rabb, ..) is ignored and reused without mentioning the origin. On September 2016 and March 2017 I had a mail exchange about Martian stromatolite candidates with professor Kranendonk who is now the Director of The Australian Centre for Astrobiology . Back on 2017 Kranendonk was skeptical about possible stromatolites on Mars on his reply to me, but now Kranendonk is now guiding storomatolite identification for Mars 2020 and ExoMars missions.