This is a really unique and creative idea - I think it could actually do really well if you give it the required time and polish you'd need to make it a viable product.
You think so? I hope! I guess the main target group is children.
I will try to polish it as much as possible before release, yes, well said! -- it is mainly a work of love anyway... I'll just have to keep going and not take so many long breaks as I've been prone to doing...
As you explained before, I'm sure it's difficult to "polish" everything, when you really have no direct control over the final results of the crosses - but I think the "cartoony" look is definitely the right approach, as it will allow you more room for error, since even a weirdly "defective" animal could end up being cute and interesting.
Thanks for your input on this question. I hope I am on the right track then...
Will there be any other features other than just randomly generating the animals? Like a place to keep them or interact with them?
The main plan for other features that I had so far was for a game mode where you would play as the mad geneticist. In this mode, you would breed towards certain goals (such as, for example: "Create an animal with four eyes, brown skin, and wings!"). Reaching these goals would give you research grant money, which you could then invest in new base animals for more genetic material to work with, or in new equipment for your lab which would allow you to manipulate the animals in more flexible ways.
This way, I would be able to introduce the various features of the game (such as cross-breeding, cloning, radiation and gene insertion) gradually to the player, and it would also probably keep the player occupied with the game for a longer time, diminishing the risk that he/she get tired of the whole thing too quickly.
The main problem with this "management mode" idea is that the current animal format is so general that it is hard to even formulate the goals for breeding: that is, "eyes" aren't really eyes, for example, but just general body parts, so if the player did breed an animal that looked like it had four eyes, there would be no certain way for the game to detect this easily, as the "eyes" might not be marked as "eyes" specifically in the code.
Also, I'm trying not to be too ambitious to begin with, before I know what reception the game will get. So for the initial demo/beta, there will probably just be animal creation, hopefully in a way that does not feel wholly "random" to the player -- he/she will still preferably be breeding towards specific goals, only that those goals will have to be up to him/her completely.
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I fixed the "lumpy foot" bug and did some other improvements. Now onto a big addition to the animal format...
Here are a few rhinoceorses again, to show the kinds of variations you can get when cross-breeding, even without radiation:

