1. There are three states: living, dead, and destructive.
2. A living cell does not die unless it has k or more destructive neighbors. If it does not have s living neighbors, it becomes a destructive cell in the next generation.
3. If a destructive cell has one or more living neighbors, it dies.
4. A cell is born if it has less than f destructive neighbors and has b living neighbors.
Of course, the natural thing to do would be to try to make a rule like Brian's Brain. B2/S/K1/F2 seems to be the rule most like Brian's Brain, although it has much more oscillator variety. It is somewhat like 2x2 in that you can make arbitarily long period oscillators in this rule.
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x = 192, y = 192, rule = B2SK1F2 .A$A$3.A$2.A$5.A$4.A$7.A$6.A$9.A$8.A$11.A$10.A$13.A$12.A$15.A$14.A$ 17.A$16.A$19.A$18.A$21.A$20.A$23.A$22.A$25.A$24.A$27.A$26.A$29.A$28.A $31.A$30.A$33.A$32.A$35.A$34.A$37.A$36.A$39.A$38.A$41.A$40.A$43.A$42. A$45.A$44.A$47.A$46.A$49.A$48.A$51.A$50.A$53.A$52.A$55.A$54.A$57.A$ 56.A$59.A$58.A$61.A$60.A$63.A$62.A$65.A$64.A$67.A$66.A$69.A$68.A$71.A $70.A$73.A$72.A$75.A$74.A$77.A$76.A$79.A$78.A$81.A$80.A$83.A$82.A$85. A$84.A$87.A$86.A$89.A$88.A$91.A$90.A$93.A$92.A$95.A$94.A$97.A$96.A$ 99.A$98.A$101.A$100.A$103.A$102.A$105.A$104.A$107.A$106.A$109.A$108.A $111.A$110.A$113.A$112.A$115.A$114.A$117.A$116.A$119.A$118.A$121.A$ 120.A$123.A$122.A$125.A$124.A$127.A$126.A$129.A$128.A$131.A$130.A$ 133.A$132.A$135.A$134.A$137.A$136.A$139.A$138.A$141.A$140.A$143.A$ 142.A$145.A$144.A$147.A$146.A$149.A$148.A$151.A$150.A$153.A$152.A$ 155.A$154.A$157.A$156.A$159.A$158.A$161.A$160.A$163.A$162.A$165.A$ 164.A$167.A$166.A$169.A$168.A$171.A$170.A$173.A$172.A$175.A$174.A$ 177.A$176.A$179.A$178.A$181.A$180.A$183.A$182.A$185.A$184.A$187.A$ 186.A$189.A$188.A$191.A$190.A!
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x = 12, y = 11, rule = B2SK1F2 .2A2$A2.A$4.A$5.A$6.A$7.A$8.A$9.A$10.A$11.A!