Gene's are funny things! I can't remember off the top of my head what combinations you need for the Chestnut gene to be dominant, but like Bustino says Urban Sea was a chestnut so perhaps if the dam is carrying a chestnut gene too it is sufficient to win out.
Ask Princess
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It's pot luck Cyc which colour genes are passed on from the parents but, regardless of their (and their ancestor's) colour, if both parents pass on the chestnut gene the foal will be a chestnut.
However, If the baby receives one bay gene + one bay gene, it will appear bay in colour. This is sometimes referred to as being a "dual bay" or a "pure breeding bay". Such horses will ALWAYS produce bay offspring, because they possess no chestnut genes which are required to make a chestnut foal.
However, If the baby receives one bay gene + one bay gene, it will appear bay in colour. This is sometimes referred to as being a "dual bay" or a "pure breeding bay". Such horses will ALWAYS produce bay offspring, because they possess no chestnut genes which are required to make a chestnut foal.
Looking at Frankel's pedigree, the line is predominantly bay. Urban Sea (grand-dam) on his sire's side and Rockfest (great-grand-dam) on his dam's side are the two most recent chestnuts in his direct line.
It's impossible to tell where the chestnut gene that Frankel is passing on comes from: Kind has produced one chestnut offspring from her six offspring, Frankel's full-brother the unraced 3yo Proconsul, so she must carry a chestnut gene herself either passed down from Rockfest to Rainbow Lake, or inherited by Rainbow Lake from her sire Rainbow Quest (whose own sire, Blushing Groom was chestnut).
It's impossible to tell where the chestnut gene that Frankel is passing on comes from: Kind has produced one chestnut offspring from her six offspring, Frankel's full-brother the unraced 3yo Proconsul, so she must carry a chestnut gene herself either passed down from Rockfest to Rainbow Lake, or inherited by Rainbow Lake from her sire Rainbow Quest (whose own sire, Blushing Groom was chestnut).
It's come from Frankel and the mare Princess. They would both need to pass on chestnut genes to produce a chestnut. So Frankel and the mare have had a chestnut gene passed down from their ancestors. If either Frankel or the mare had passed down a bay gene the foal would have been bay. That's how I understand it.
Oh I agree with that Ron, there needs to be a chestnut gene on both sides. I was just saying there's no way of knowing whether the gene from Frankel comes from his sire line or dam line. Both Galileo and Kind carry one copy of the gene (as they've both produced chestnut progeny) but who knows who gave him the bay gene and who gave him the chestnut one.
Now there's a challenge. One I can't cope with tonight as I'm off to bed. Might have a go tomorrow but maybe it's insoluble
Think I'll take the easy route and assume it's insoluble. Actually, unless someone has actually tracked the colour genes passed on through generations I'm not sure how any conclusions as to which combination of genes produce which colour have been reached. Is this something they analyse on dead horses Princess?
All pretty simple Ron. 
Base Color
Every horse has a base color, which can be black, bay, or red. This is controlled by the Extension (Red/Black Factor) and Agouti genes. The Extension gene controls the production of black or red pigment throughout the coat. The allele for black color (E) is dominant over the red allele (e), so a horse only needs one copy of the black allele to appear black-based.
The Agouti gene can then modify black pigment by pushing it the the points of the horse, creating a bay. The Agouti gene is dominant, so a black pigmented horse only needs one copy of the Agouti gene (A) to appear bay. Agouti does not have any effect on red pigment.
There may be some variation in the intensity of the base colors, for example, dark bays compared to light bays or liver chestnuts to sorrels. This could be caused by a variation in the expression of the genes or interaction of other genetic factors.
Horse Base Coat Red/Black Factor Agouti
Solid Black EE or Ee aa
Bay or Brown EE or Ee AA or Aa
Red (Chestnut/Sorrel) ee AA, Aa, or aa
Base Color
Every horse has a base color, which can be black, bay, or red. This is controlled by the Extension (Red/Black Factor) and Agouti genes. The Extension gene controls the production of black or red pigment throughout the coat. The allele for black color (E) is dominant over the red allele (e), so a horse only needs one copy of the black allele to appear black-based.
The Agouti gene can then modify black pigment by pushing it the the points of the horse, creating a bay. The Agouti gene is dominant, so a black pigmented horse only needs one copy of the Agouti gene (A) to appear bay. Agouti does not have any effect on red pigment.
There may be some variation in the intensity of the base colors, for example, dark bays compared to light bays or liver chestnuts to sorrels. This could be caused by a variation in the expression of the genes or interaction of other genetic factors.
Horse Base Coat Red/Black Factor Agouti
Solid Black EE or Ee aa
Bay or Brown EE or Ee AA or Aa
Red (Chestnut/Sorrel) ee AA, Aa, or aa
Clear as mud!
Cyc, I've just read the following write up on SO YOU THINK's prospects as a first season sire in Europe:
SO YOU THINK (NZ) (High Chaparral {Ire}--Triassic {NZ}, by Tights)
2013 fee: €17,500 (Coolmore)
First crop: 68 to race Yearling sales: 35,674gns/€48,321 for 33 sold
Emma Berry: The death of High Chaparral in December 2014 cut short the career of a stallion whose worth was never fully appreciated in his lifetime, but the likes of Free Eagle (Ire) in the Northern Hemisphere and Contributer (Ire) in Australia have continued to illustrate how big a loss he was. Ironically, given the relative lack of popularity of the Sadler's Wells line in Australia at the time, it was in the Southern Hemisphere where High Chaparral first properly made a name for himself, and the very best of some decent progeny from his shuttling days is So You Think. The dark brown stallion with the wildly long mane was the toast of Bart Cummings's stable during the first half of his racing career, which saw him win five Group 1 races, including the Cox Plate twice. His switch north to Aidan O'Brien at Ballydoyle may have been the cause of some angst for his Australian fans at the time, but he proved more than equal to the challenge, adding another five Group 1s to his name and beating the likes of Derby winner Workforce (GB) and dual Oaks heroine Snow Fairy (Ire) in doing so.
So You Think's first covering season at Coolmore's Irish base had a delayed start after he injured a hock, so he will be at a disadvantage numerically this season, but his 2-year-olds have found their way into some powerful stables.
His first Southern Hemisphere crop has already produced the G2 Matamata Breeders S. winner Gold Rush (NZ) in New Zealand as well as Flemington listed race runner-up Conscious (Aus) from just a handful of runners.
Bill Oppenheim: Has the best credentials of any Australasian-bred to stand 'up north' in many years, winning 10 Group 1's and running RPR's between 127-129 in 10 of his last 11 turf starts. Not especially commercial but if he passes along his toughness, durability, and class he'll make a sire
Cyc, I've just read the following write up on SO YOU THINK's prospects as a first season sire in Europe:
SO YOU THINK (NZ) (High Chaparral {Ire}--Triassic {NZ}, by Tights)
2013 fee: €17,500 (Coolmore)
First crop: 68 to race Yearling sales: 35,674gns/€48,321 for 33 sold
Emma Berry: The death of High Chaparral in December 2014 cut short the career of a stallion whose worth was never fully appreciated in his lifetime, but the likes of Free Eagle (Ire) in the Northern Hemisphere and Contributer (Ire) in Australia have continued to illustrate how big a loss he was. Ironically, given the relative lack of popularity of the Sadler's Wells line in Australia at the time, it was in the Southern Hemisphere where High Chaparral first properly made a name for himself, and the very best of some decent progeny from his shuttling days is So You Think. The dark brown stallion with the wildly long mane was the toast of Bart Cummings's stable during the first half of his racing career, which saw him win five Group 1 races, including the Cox Plate twice. His switch north to Aidan O'Brien at Ballydoyle may have been the cause of some angst for his Australian fans at the time, but he proved more than equal to the challenge, adding another five Group 1s to his name and beating the likes of Derby winner Workforce (GB) and dual Oaks heroine Snow Fairy (Ire) in doing so.
So You Think's first covering season at Coolmore's Irish base had a delayed start after he injured a hock, so he will be at a disadvantage numerically this season, but his 2-year-olds have found their way into some powerful stables.
His first Southern Hemisphere crop has already produced the G2 Matamata Breeders S. winner Gold Rush (NZ) in New Zealand as well as Flemington listed race runner-up Conscious (Aus) from just a handful of runners.
Bill Oppenheim: Has the best credentials of any Australasian-bred to stand 'up north' in many years, winning 10 Group 1's and running RPR's between 127-129 in 10 of his last 11 turf starts. Not especially commercial but if he passes along his toughness, durability, and class he'll make a sire
They've mapped the equine genome, so I'm sure someone out there has been taking DNA samples from the high profile horses to see if they can identify a "Racing Gene". Colour, and its inheritable characteristics, is a good place to start when trying to map out things like this. I might have a look and see if I can find any articles on it.
Looking a bit further at SO YOU THINK, as said in that article his first book was curtailed due to injury (68 foals from 83 mares); in his second book he covered 102 and in his third book 68.
Glancing at the breeders that sent him mares, he attracted a good number of owner/breeders including the Queen, Gestut Ammerland, Highclere Stud, Littleton Stud and Woodcote Stud. A few jumping breeders too such as Gigginstown House and the Kelvin-Hughes'. There are a decent number of Coolmore aliases listed so they definitely supported him with their own mares, though they may well have sold a good number of these. He also got a reasonable number of overseas breeders including 4 from Germany, 2 from Italy and even Calumet Farm in the US sent him a mare - RESTLESS RIXA a maiden winner in France who produced the Prix Djebel 3rd REDEMPTOR.
Glancing at the breeders that sent him mares, he attracted a good number of owner/breeders including the Queen, Gestut Ammerland, Highclere Stud, Littleton Stud and Woodcote Stud. A few jumping breeders too such as Gigginstown House and the Kelvin-Hughes'. There are a decent number of Coolmore aliases listed so they definitely supported him with their own mares, though they may well have sold a good number of these. He also got a reasonable number of overseas breeders including 4 from Germany, 2 from Italy and even Calumet Farm in the US sent him a mare - RESTLESS RIXA a maiden winner in France who produced the Prix Djebel 3rd REDEMPTOR.
Juddmonte have tweeted this picture of their home-bred mare RESPONSIBLE (the last foal produced by Hasili, by Oasis Dream but unraced) and her first foal, a filly by Frankel.
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Frankel, Hasili and Oasis Dream: in three names the best three families of Juddmonte's European operation. A lot rests on this little girl. Fortunately she doesn't know.